Question

Solve the following using substitutionY = -2X + 10.5x - y = 4

Answer 1

We are to solve the equations

`\begin{gathered} y=-2x+1 \\ 0.5x-y=4 \end{gathered}`

The equation can be rewritten as

`\begin{gathered} y+2x=1------------\text{equation 1} \\ -y+0.5x=4-----------\text{equation 2} \end{gathered}`

Using substitution method

From equation 1

`y=1-2x--------\text{equation 3}`

Substitute 1 - 2x for y into equation 2

This gives

`\begin{gathered} -(1-2x)+0.5x=4 \\ -1+2x+0.5x=4 \\ -1+2.5x=4 \\ 2.5x=4+1 \\ 2.5x=5 \\ x=(5)/(2.5) \\ x=2 \end{gathered}`

Therefore, x = 2

Substitute 2 for x into equation 3

This gives

`\begin{gathered} y=1-2(2) \\ y=1-4 \\ y=-3 \end{gathered}`

Therefore the solution to the equations is

x = 2, y = -3