Question

Solve the following system of equations by using elimination: x + 2y = 8 -x - 3y = 2

Answer 1

Solve the following system of equations by using elimination:

`\begin{cases}x+2y=8\ldots\ldots\text{.}(1) \\ -x-3y=2\ldots\ldots(11)\end{cases}`

Using Elimination method:

`\begin{gathered} \begin{cases}x+2y=8 \\ (-x-3y=2)/(-y=10)\end{cases}\text{+} \\ \text{divide both side by -1} \\ -(y)/(-1)=(10)/(-1) \\ y=-10 \end{gathered}`

Substitute the value of y in equation (1):

`\begin{gathered} x_{}+2y=8 \\ x+2(-10)=8 \\ x-20=8 \\ x=8+20 \\ x=28 \end{gathered}`

Therefore the value of x = 28 and y = -10

Hence the correct answer is (x,y) = (28,-10)