Question

Solve using elimination. 4x – 4y = 12 3x – 4y = 4 (_ , _)

Answer 1

`\begin{gathered} 4x-4y=12 \\ 3x-4y=4 \end{gathered}`

In solving by elimination, we have to use either one of the two given equation to express one variable in terms of the other variable. Let's use the first one to express x in terms of y

`\begin{gathered} 4x-4y=12 \\ 4x=12+4y \\ (4x)/(4)=(12+4y)/(4) \\ x=3+y \end{gathered}`

Now that we have the value of x, we will have to substitute it in the second equation.

`\begin{gathered} 3x-4y=4 \\ 3(3+y)-4y=4_{} \\ 9+3y-4y=4 \\ 9-y=4 \\ -y=4-9 \\ -y=-5 \\ -(y)/(-1)=-(5)/(-1) \\ y=5 \end{gathered}`

Now that we solved for y, we can substitute its value on the expression for x that we derived from the first equation.

`\begin{gathered} x=3+y \\ x=3+5 \\ x=8 \end{gathered}`

In order to check if the values of x and y are correct, we can substitue it in either of the two equations to see if it will satisfy the equation. Let's use the second equation to illustrate this.

`\begin{gathered} 3x-4y=4 \\ 3(8)-4(5)=4 \\ 24-20=4 \\ 4=4 \end{gathered}`

The value of x and y that we calculated satisfy the equation. Therefore, the answer is :

`\begin{gathered} x=8 \\ y=5 \end{gathered}`