Solution: The given equations are $\begin{array}{l} \frac{x}{a}+\frac{y}{b}=\mathrm{a}+\mathrm{b}\dots \dots(i) \\ \frac{x}{a^{2}}+\frac{y}{b^{2}}=2\dots \dots(ii) \end{array}$ Multiplying...

Solution: The given equations are $\begin{array}{l} a^{2} x+b^{2} y=c^{2}\dots \dots (i) \\ b^{2} x+a^{2} y=d^{2} \dots \dots(ii) \end{array}$ Multiplying equation(i) by $\mathrm{a}^{2}$ and...

Solution: The given equations are $\begin{array}{l} \mathrm{x}+\mathrm{y}=\mathrm{a}+\mathrm{b} \quad\{\ldots \ldots(i) \\ \mathrm{ax}-\mathrm{by}=\mathrm{a}^{2}-\mathrm{b}^{2}+\ldots \ldots(ii) \\...

Solution: The given eq. are: $\frac{b x}{a}+\frac{a y}{b}=\mathrm{a}^{2}+\mathrm{b}^{2}$ By taking LCM, we obtain: $\begin{array}{l} \frac{b^{2} x+a^{2} y}{a b}=a^{2}+b^{2} \\ \Rightarrow b^{2}...

Solution: The given equations are: $\frac{b x}{a}-\frac{a y}{b}+a+b=0$ By taking LCM, we obtain: $b^{2} x-a^{2} y=-a^{2} b-b^{2} a\dots \dots(i)$ and $b x-a y+2 a b=0$ $b x-a y=-2 a b\dots...

Solution: The given equations are $\begin{array}{l} a x-b y=a^{2}+b^{2}\dots \dots(i) \\ x+y=2 a\dots \dots(ii) \end{array}$ From equation(ii) $y=2 a-x$ Substituting $\mathrm{y}=2...

Solution: The given equations are $\begin{array}{l} 6(a x+b y)=3 a+2 b \\ \Rightarrow 6 a x+6 b y=3 a+2 b\dots \dots(i) \end{array}$ and $6(b x-a y)=3 b-2 a$ $\Rightarrow 6 b x-6 a y=3 b-2 a\dots...

Solution: The given eq. can be written as $\begin{array}{l} \frac{x}{a}-\frac{y}{b}=0\dots \dots(i) \\ a x+b y-u^{2}+b^{2}\dots \dots(ii) \end{array}$ From equation(i), $\mathrm{y}=\frac{b x}{a}$...

Solution: The given equations are $\begin{array}{l} \mathrm{px}+\mathrm{qy}=\mathrm{p}-\mathrm{q}\dots \dots(i) \\ \mathrm{qx}-\mathrm{py}=\mathrm{p}+\mathrm{q}\dots \dots(ii) \end{array}$...

Solution: The given equations are: $\begin{array}{l} \frac{x}{a}+\frac{y}{b}=2 \\ \Rightarrow \frac{b x+a y}{a b}=2 \quad[\text { Taking LCM }] \\ \Rightarrow \mathrm{bx}+\mathrm{ay}=2 \mathrm{ab}...

Solution: The given equations are $\begin{array}{l} \mathrm{x}+\mathrm{y}=\mathrm{a}+\mathrm{b}\dots \dots(i) \\ \mathrm{ax}-\mathrm{by}=\mathrm{a}^{2}-\mathrm{b}^{2}\dots \dots(ii) \end{array}$...

Solution: The given equations can be written as $\begin{array}{l} \frac{3}{x}+\frac{6}{y}=7\dots \dots(i) \\ \frac{9}{x}+\frac{3}{y}=11\dots \dots(ii) \end{array}$ Multiplying equation(i) by 3 and...

Solution: The given equations are $\begin{array}{l} \frac{2}{3 x+2 y}+\frac{3}{3 x-2 y}=\frac{17}{5}\dots \dots(i) \\ \frac{5}{3 x+2 y}+\frac{1}{3 x-2 y}=2\dots \dots(ii) \end{array}$ Substituting...

Solution: The given equations are $\begin{array}{l} \frac{1}{2(x+2 y)}+\frac{5}{3(3 x-2 y)}=-\frac{3}{2}\dots \dots(i) \\ \frac{1}{4(x+2 y)}-\frac{3}{5(3 x-2 y)}=\frac{61}{60}\dots \dots(ii)...

Solution: The given equations are $\begin{array}{l} \frac{1}{3 x+y}+\frac{1}{3 x-y}=\frac{3}{4}\dots \dots(i) \\ \frac{1}{2(3 x+y)}-\frac{1}{2(3 x-y)}=-\frac{1}{8} \end{array}$ $\frac{1}{3...

Solution: The given equations can be written as $\begin{array}{l} \frac{5}{x}+\frac{2}{y}=6\dots \dots (i) \\ \frac{-5}{x}+\frac{4}{y}=-3\dots \dots(ii) \end{array}$ Adding equation(i) and...

Solution: The given equations are: $23 x-29 y=98 \quad \ldots .$ (i) $29 x-23 y=110 \ldots \ldots$ (ii) Adding equation(i) and equation(ii), we obtain: $\begin{array}{l} 52 x-52 y=208 \\ \Rightarrow...

Solution: The given equations are: $\begin{aligned} 217 \mathrm{x}+131 \mathrm{y} =913\dots \dots(i) \\ 131 \mathrm{x}+217 \mathrm{y} =827 \ldots \text {....(ii) } \end{aligned}$ On adding...

Solution: The given eq. are: $\begin{array}{l} 71 x+37 y=253\dots \dots(i) \\ 37 x+71 y=287 \ldots \ldots \text {...(ii) } \end{array}$ On adding equation(i) and equation(ii), we obtain:...

Solution: The given equations are $\frac{10}{x+y}+\frac{2}{x-y}=4 \quad \ldots \ldots$ (i) $\frac{15}{x+y}-\frac{9}{x-y}=-2\dots \dots(ii)$ Substituting $\frac{1}{x+y}=\mathrm{u}$ and...

Solution: The given eq. are $\frac{44}{x+y}+\frac{30}{x-y}=10 \dots \dots(i)$ $\frac{55}{x+y}-\frac{40}{x-y}=13\dots \dots (ii)$ Putting $\frac{1}{x+y}=u$ and $\frac{1}{x-y}=v$, we get: $44 u+30...

Solution: The given eq. are $\frac{5}{x+1}+\frac{2}{y-1}=\frac{1}{2} \quad \ldots \ldots$ (i) $\frac{10}{x+1}-\frac{2}{y-1}=\frac{5}{2}\dots \dots (ii)$ On substituting $\frac{1}{x+1}=\mathrm{u}$...

Solution: The given eq. are $\begin{array}{l} \frac{3}{x+y}+\frac{2}{x-y}=2  \ldots \ldots \text { (i) } \\ \frac{9}{x+y}-\frac{4}{x-y}=1  \ldots \ldots \text { (ii) } \end{array}$ Substituting...

Solution: The given eq. are $\frac{5}{x+y}-\frac{2}{x-y}=-1 \quad \ldots \ldots \text { (i) }$ $\frac{15}{x+y}-\frac{7}{x-y}=10\dots \dots(ii)$ Substituting $\frac{1}{x+y}=\mathrm{u}$ and...

Solution: The given eq. are: $x + y = 5xy \dots \dots(i)$ $3x + 2y = 13xy \dots \dots(ii)$ From equation (i), we have: $\begin{array}{l} \frac{x+y}{x y}=5 \\ \Rightarrow \frac{1}{y}+\frac{1}{x}=5...

Solution: The given eq. are: $\begin{array}{l} 4 x+6 y=3 x y \quad \ldots \ldots(i) \\ 8 x+9 y=5 x y \quad \ldots \ldots(i i) \end{array}$ From eq. (i), we have: $\begin{array}{l} \frac{4 x+6 y}{x...

Solution: The given eq. are: $\begin{array}{l} \frac{3}{x}+\frac{2}{y}=12 \ldots \ldots \ldots \text { (i) } \\ \frac{2}{x}+\frac{3}{y}=13 \ldots \ldots . \text { (ii) } \end{array}$ Multiplying...

Solution: The given eq. are: $\begin{array}{l} \frac{5}{x}-\frac{3}{y}=1 \ldots \ldots(i) \\ \frac{3}{2 x}+\frac{2}{3 y}=5 \ldots \ldots (ii) \end{array}$ Putting $\frac{1}{x}=u$ and...

Solution: The given eq. are: $\begin{array}{l} \frac{9}{x}-\frac{4}{y}=8 \ldots \ldots . .(i) \\ \frac{13}{x}+\frac{7}{y}=101 \ldots \ldots (ii) \end{array}$ Putting $\frac{1}{x}=u$ and...

Solution: The given eq. are: $\begin{array}{l} \frac{3}{x}-\frac{1}{y}+9=0 \\ \Rightarrow \frac{3}{x}-\frac{1}{y}=-9 \quad \ldots \ldots(i) \\ \Rightarrow \frac{2}{x}-\frac{3}{y}=5 \ldots \ldots...

Solution: The given eq. are: $\begin{array}{l} 2 x-\frac{3}{y}=9 \ldots \ldots \text { (i) } \\ 3 x+\frac{7}{y}=2 \ldots \ldots \text { (ii) } \end{array}$ Putting $\frac{1}{y}=\mathrm{v}$, we...

Solution: The given eq. are: $\begin{array}{l} x+\frac{6}{y}=6 \quad \ldots \ldots \text {(i) } \\ 3 x-\frac{8}{y}=5 \ldots \ldots \text { (ii) } \end{array}$ Putting $\frac{1}{y}=\mathrm{v}$, we...

Solution: The given eq. are: $\begin{array}{l} \frac{5}{x}+6 y=13 \ldots \ldots \text { (i) } \\ \frac{3}{x}+4 y=7 \ldots \ldots \text { (ii) } \end{array}$ Putting $\frac{1}{x}=\mathrm{u}$, we...

Solution: The given eq. are: $\frac{x+y-8}{2}=\frac{x+2 y-14}{3}=\frac{3 x+y-12}{11}$ i.e., $\frac{x+y-8}{2}=\frac{3 x+y-12}{11}$ On cross multiplication, we obtain: $\begin{array}{l} 11 x+11 y-88=6...

Solution: The given equations are: $\begin{array}{l} 6 x+5 y=7 x+3 y+1=2(x+6 y-1) \\ \Rightarrow 6 x+5 y=2(x+6 y-1) \\ \Rightarrow 6 x+5 y=2 x+12 y-2 \\ \Rightarrow 6 x-2 x+5 y-12 y=-2 \\...

Solution: The given eq. are: $7(y + 3) – 2(x + 2) = 14$ $\Rightarrow 7y + 21 – 2x – 4 = 14$ $\Rightarrow -2x + 7y = -3 \dots \dots(i)$ and $4(y – 2) + 3(x – 3) = 2$ $\Rightarrow 4y – 8 + 3x – 9 = 2$...

Solution: The given system of eq. is $0.3 \mathrm{x}+0.5 \mathrm{y}=0.5\dots \dots(i)$ $0.5 \mathrm{x}+0.7 \mathrm{y}=0.74 \dots \dots(ii)$ On multiplying equation(i) by 5 and equation(ii) by 3 and...

Solution: The given system of eq. is $0.4x + 0.3y = 1.7 \dots \dots(i)$ $0.7x – 0.2y = 0.8 \dots \dots(ii)$ On multiplying equation(i) by $0.2$ and equation(ii) by $0.3$ and adding them, we obtain...

Solution: The given eq. are: $\begin{array}{l} \frac{7-4 x}{3}=y \\ \Rightarrow 4 x+3 y=7 \dots \dots(i) \end{array}$ $\begin{array}{l} \text { and } 2 x+3 y+1=0 \\ \Rightarrow 2 x+3 y=-1 \ldots...

Solution: The given eq. are; $\begin{array}{l} 2 x-5 y=\frac{8}{3} \ldots \ldots(i) \\ 3 x-2 y=\frac{5}{6} \ldots \cdots . . \text { (ii) } \end{array}$ On multiplying equation(i) by 2 and...

Solution: The given eq. are: $\begin{array}{l} 2 \mathrm{x}-\frac{3 y}{4}=3 \ldots \ldots(\mathrm{i}) \\ 5 \mathrm{x}=2 \mathrm{y}+7 \ldots \ldots \text { (ii) } \end{array}$ When multiplying...

Solution: The given system of eq. is: $\begin{array}{ll} 4 \mathrm{x}-3 \mathrm{y}=8 & \ldots \ldots \text { (i) } \\ 6 \mathrm{x}-\mathrm{y}=\frac{29}{3} & \ldots \ldots \text { (ii) }...

Solution: The given eq. are: $\begin{array}{l} \frac{x}{3}+\frac{y}{4}=11 \\ \Rightarrow 4 x+3 y=132 \ldots \ldots(i) \end{array}$ and $\frac{5 x}{6}-\frac{y}{3}+7=0$ $\Rightarrow 5 x-2 y=-42 \ldots...

Solution: The given system of eq. can be written as: $\begin{array}{cc} 9 \mathrm{x}-2 \mathrm{y}=108 & \ldots \ldots \text { (i) } \\ 3 \mathrm{x}+7 \mathrm{y}=105 & \ldots \text {..(ii) }...

Solution: The given system of eq. is: $\begin{array}{l} 2 x-y+3=0 \ldots \ldots(i) \\ 3 x-7 y+10=0 \ldots \ldots(i i) \end{array}$ From equation(i), write y in terms of $x$ to obtain $y=2 x+3$ On...

Solution: The given system of equation is: $\begin{array}{c} 3 \mathrm{x}-5 \mathrm{y}-19=0 \\ -7 \mathrm{x}+3 \mathrm{y}+1=0 \end{array}$ When multiplying equation(i) by 3 and equation(ii) by 5 ,...

Solution: The given system of eq. is: $\begin{array}{cc} 2 \mathrm{x}-3 \mathrm{y}=13 & \ldots \ldots \text { (i) } \\ 7 \mathrm{x}-2 \mathrm{y}=20 & \ldots \ldots \text { (ii) }...

Solution: The given system of equation is: $\begin{array}{l} 2 x+3 y=0 & \ldots \ldots \text { (i) } \\ 3 x+4 y=5 & \ldots \text {..(ii) } \end{array}$ When multiplying equation(i) by 4 and...

Solution: The given system of equations is $x-y=3 \dots \dots(i)$ $\frac{x}{3}+\frac{y}{2}=6 \dots \dots(ii)$ From equation(i), write y in terms of $x$ to obtain $y=x-3$ When substituting...

Solution: The given system of equation is: $\mathrm{x}+\mathrm{y}=3 \ldots \ldots \text { (i) }$ $4 x-3 y=26 \ldots \ldots \text { (ii) }$ When multiplying equation(i) by 3 , we obtain: $3 x+3 y=9...