Question

Solve by elimination - 4x- 8y=83x- 5y=16

Answer 1

See below

Explanation:

-4x -8y = 8

3x-5y = 16 <===== multiply this equation by 4/3 to get

4x - 20/3 y = 64/3 <=====add to first equation...this will eliminate 'x'

-8y - 20/3 y = 8 + 64/3 solve for y = -2

use this value of y in any of the equations to compute x

-4x - 8(-2) = 8

-4x = 8-16 shows x = 2

Answer 2

Given the system of equations:

`\begin{gathered} -4x-8y=8 \\ 3x-5y=16 \end{gathered}`

The solution of the system will be as follows:

`\begin{gathered} -4x-8y=8\rightarrow*3 \\ 3x-5y=16\rightarrow*4 \\ ------------ \\ -12x-24y=24 \\ 12x-20y=64 \\ ------------ \\ (12x-12x)+(-24y-20y)=24+64 \\ \\ -44y=88 \\ \\ y=(88)/(-44)=-2 \end{gathered}`

Substitute with y into the first equation to find x:

`\begin{gathered} -4x-2\cdot-8=8 \\ -4x+16=8 \\ -4x=8-16 \\ -4x=-8 \\ \\ x=(-8)/(-4)=2 \end{gathered}`

So, the solution of the system is:

`\begin{gathered} x=2 \\ y=-2 \\ (x,y)=(2,-2) \end{gathered}`