The solution of equations 3x+2y=10 and 4x-2y=4 is

# The solution of equations $3x+2y=10$ and $4x-2y=4$ is

1. A
$x=-2$ and $y=2$
2. B
$x=2$ and $y=-2$
3. C
$x=-2$ and $y=-2$
4. D
$x=2$ and $y=2$

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### Solution:

$3x+2y=10$ and $4x-2y=4$ Comparing with ${a}_{1}x+{b}_{1}y+{c}_{1}=0$ and ${a}_{2}x+{b}_{2}y+{c}_{2}=0$, we get
${a}_{1}=3,$ ${b}_{1}=2$ and ${c}_{1}=-10$
${a}_{2}=4,$ ${b}_{2}=-2$ and ${c}_{2}=-4$
By cross-multiplication formula, we have

$\frac{x}{\left(2\right)\left(-4\right)-\left(-2\right)\left(-10\right)}=\frac{y}{\left(-10\right)\left(4\right)-\left(3\right)\left(-4\right)}=\frac{1}{\left(-2\right)\left(3\right)-\left(4\right)\left(2\right)}$
$\frac{x}{-28}=\frac{y}{-28}=\frac{1}{-14}$ $x=\frac{-28}{-14}$ and $y=\frac{-28}{-14}$
$x=2$ and $y=2$
Therefore, 4 is the correct option.

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