Question

Use elimination to solve the following system of equations 2x - y = 7 and -2x+ 3y = 9.(8,9)(3,0)(7.5, 8)(7,9)I am not sure if my answer is right please help me

Answer 1

Write out the two-equation given

`\begin{gathered} 2x-y=7-----equation(1) \\ -2x+3y=9------\text{equation}(2) \end{gathered}`

In other to use the elimination method, we ensure that one of the variables in the two-equation has the same coefficient.

By observation, it can be seen that the coefficient of the x in the two equations is the same. So we add two equations together because they have different signs to eliminate x

i.e.

`\text{equation}(1)+\text{equation}(2)`

Therefore,

`\begin{gathered} 2x+(-2x)-y+(+3y)=7+9 \\ -y+3y=16 \\ 2y=16 \\ y=(16)/(2) \\ y=8 \end{gathered}`

Substitute the value of y in any of the two equations to get the value of x. Let us pick equation(1)

`\begin{gathered} 2x-y=7 \\ y=8 \\ 2x-8=7 \\ 2x=7+8 \\ 2x=15 \end{gathered}`
`\begin{gathered} x=(15)/(2) \\ x=7.5 \end{gathered}`

Hence, x=7.5, y=8 (7.5,8)