# How do you solve the following system: 4x-2y=4 , 3x -2y=24 ?

May 8, 2016

Solution is $\left(- 20 , - 42\right)$

#### Explanation:

In the given system of equations $4 x - 2 y = 4$ and $3 x - 2 y = 24$, we can solve them by first eliminating one variable, which will give the value of other variable. This value when put in either equation should give us the value of eliminated variable.

In the given system of equations, as coefficients of $y$ are same, we can eliminate $y$ simply by subtracting second equation from first equation, which gives us

$4 x - 2 y - \left(3 x - 2 y\right) = 4 - 24$ or

$4 x - 2 y - 3 x + 2 y = - 20$ or $x = - 20$.

Now putting this in first equation, we get

$4 \cdot \left(- 20\right) - 2 y = 4$ or $- 80 - 2 y = 4$ or

$2 y = - 80 - 4 = - 84$ or $y = - 42$

Hence solution is $\left(- 20 , - 42\right)$

graph{(4x-2y-4)(3x-2y-24)=0 [-160, 160, -80, 80]}