Question

Solve the system of equations using elimination.8x - 5y = 13-16x - 10y = -6Show your work here:Solution:

Answer 1

Step 1:

In this question, we are given the following:

Solve the system of equations using elimination.

`\begin{gathered} \text{8 x - 5y = 13 -- equation 1} \\ -16\text{ x - 10y = - 6 -- equation 2} \end{gathered}`

Step 2:

Given,

`\begin{gathered} 8x\text{ - 5y = 13 -- equation 1} \\ \text{equation 1 multiplied by 2, we have that:} \\ 16\text{ x - 10y = 26 -- equation 3} \\ -16\text{ x -10 y = - 6 -- equation 2} \end{gathered}`
`\begin{gathered} equation\text{ 3 + equation 2, we have that:} \\ -10y\text{ + -10 y = 26 + (-6)} \\ -20y\text{ = 20} \\ \text{Divide both sides by -20, we have that:} \\ y\text{ = }(20)/(-20) \\ y\text{ = -1} \end{gathered}`

Now, since y = -1 , we put the value of y = -1 in equation 1,

`\begin{gathered} 8\text{ x- 5y = 13 --equation 1} \\ 8x\text{ - 5 ( -1 ) = 13} \\ 8x\text{ + 5 = 13} \\ 8x\text{ = 13 - 5} \\ 8\text{ x= 8} \\ \text{Divide both sides by 8 , we have that:} \\ x\text{ = }(8)/(8) \\ x\text{ = 1} \end{gathered}`

CONCLUSION:

The final answer =

`\text{ x= 1 , }y\text{ = - 1}`

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