Question

By equating coefficients of variables, solve the following equations.
(i) $3x-4y=7;5x+2y=3$
(ii) $5x+7y=17;3x-2y=4$
(iii) $x-2y=-10;3x-5y=-12$
(iv) $4x+y=34;x+4y=16$

Answer 1

(i) $3x-4y=7;5x+2y=3$

$3x-4y=7\Rightarrow$ $3x-4y=7$

$2(5x+2y=3)\Rightarrow$ $10x+4y=6$

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$13x+0=13$

$x=1$ $\Rightarrow$ $5+2y=3\Rightarrow$ $y=-1$

$\therefore$ $(x,y)=(1,-1)$

(ii) $5x+7y=17;3x-2y=4$

$3(5x+7y=17)\Rightarrow 15x+21y=51$

$5(3x-2y=4)\Rightarrow 15x-10y=20$

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$31y=31\Rightarrow$ $y=1\Rightarrow$ $3\left(x\right)-2=4\Rightarrow$ $x=2$

$\therefore$ $(x,y)=(2,1)$

(iii) $x-2y=-10;3x-5y=-12$

$3(x-2y=-10)\Rightarrow$ $3x-6y=-30$

$3x-5y=-12$

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$-x=18\Rightarrow x=18$

$18-2y=-10\Rightarrow$ $y=14$

$\therefore$ $(x,y)=(18,14)$

(iv) $4x+y=34;x+4y=16$

$4x+y=34\Rightarrow$ $4x+y=34$

$4(x+4y=16)\Rightarrow$ $4x+16y=64$

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$-15y=-30$

$\Rightarrow$ $y=2$

$4x+2=34$

$\Rightarrow$ $x=8$

$\Rightarrow$ $(x,y)=(8,2)$