# How do you solve the system of equations 5x - 2y = 12 and  2x - 3y = 7?

Mar 30, 2018

$x = 2$
$y = - 1$

#### Explanation:

=$5 x - 2 y = 12$

Multiplying above equation with $2$

• $10 x - 4 y = 24$

=$2 x - 3 y = 7$

Multiplying above equation with 5

• $10 x - 15 y = 35$

Now subtracting both equations to cancel out $10 x$

=$\left(10 x - 4 y = 24\right) - \left(10 x - 15 y = 35\right)$

=$11 y = - 11$

=$y = - 1$

Now for $x$ put y=-41 in below equation

=$2 x - 3 y = 7$

=$2 x - 3 \left(- 1\right) = 7$

=$2 x = 4$

=$x = 2$

Hope this helps!

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