Question

Use elimination to solve eachsystem of equations4x - 3y = 112x - y = -8

Answer 1

Given:

The system of equations is,

`\begin{gathered} 4x-3y=11\text{ . . . . . . (1)} \\ 2x-y=-8\text{ . . . . . .(2)} \end{gathered}`

The objective is to solve the equations using the elimination method.

Step-by-step explanation:

To solve the equations multiply the equation (2) by -3.

`\begin{gathered} -3\lbrack2x-y=-8\rbrack \\ -6x+3y=+24\text{ . . . . (3)} \end{gathered}`

On solving equations (1) and (3),

`\begin{gathered} 4x-3y=11 \\ (-6x+3y=24)/(-2x=35) \end{gathered}`

On further solving the above equation,

`x=-(35)/(2)`

Substitute the value of x in equation (2).

`\begin{gathered} 2(-(35)/(2))-y=-8 \\ -35-y=-8 \\ -y=-8+35 \\ -y=27 \\ y=-27 \end{gathered}`

Hence, the value of x is (-35/2) and the value of y is -27.