Question

Solve this system of equations byusing the elimination method.x - 5y = 164x – 2y = -8([?],

Answer 1

Given:

There are given two equations:

`\begin{gathered} x-5y=16...(1) \\ 4x-2y=-8...(2) \end{gathered}`

Step-by-step explanation:

To find the value by using the elimination method, we need to multiply by 4 into the equation (1) and 1 into the multiply by (2):

Then,

From the equation (1):

`\begin{gathered} 4(x-5y=16) \\ 4x-20y=64...(3) \end{gathered}`

And,

From the equation (2):

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

Now,

From the equation (3) and equation (4):

`4x-20y-64=4x-2y+8`

Then,

`\begin{gathered} 4x-20y-64-4x+2y-8=0 \\ -20y-64+2y-8=0 \\ -18y-72=0 \\ -18y=72 \\ y=-4 \end{gathered}`

Now,

Put the value of y into the equation (3):

`\begin{gathered} \begin{equation*} 4x-20y=64 \end{equation*} \\ 4x-20(-4)=64 \\ 4x+80=64 \\ 4x=64-80 \\ 4x=-16 \\ x=-4 \end{gathered}`

Final answer:

Hence, the value of x and y is shown below:

`(-4,-4)`