Question

A system of two equations is shown.

2 + 2y = 6
2x - 3y = 26
What is the solution of the system?
0 (-2,3)
(1, -2)
O (-2.4)
(10.-2)

Answer 1

(10 -2)

Explanation:

first you have to substitute the value of x, solve that, substitute the value of y, solve, and that’s about it. :)

Answer 2

Please check the explanation.

Explanation:

Given the system of equations

2 + 2y = 6

2x - 3y = 26

Let us solve the system of equations

`\begin{bmatrix}2+2y=6\\ 2x-3y=26\end{bmatrix}`

Rearrange equations

`\begin{bmatrix}-3y+2x=26\\ 2y=4\end{bmatrix}`

Multiply -3y+2x=26 by 2: -6y+4x=52

Multiply 2y = 4 by 3: 6y = 12

`\begin{bmatrix}-6y+4x=52\\ 6y=12\end{bmatrix}`

adding the equations

`6y=12`

`+`

`\underline{-6y+4x=52}`

`4x=64`

Solve 4x = 64 for x

`4x = 64`

divide both sides by 4

`(4x)/(4)=(64)/(4)`

Simplify

`x = 16`

For -6y+4x = 52 plug in x = 16

`-6y+4\cdot \:16=52`

Multiply the numbers: 4 · 16 = 64

`-6y+64=52`

Subtract 64 from both sides

`-6y+64-64=52-64`

Simplify

`-6y=-12`

Divide both sides by -6

`(-6y)/(-6)=(-12)/(-6)`

`y=2`

Therefore, the solution to the system of equations be:

`y=2,\:x=16`

Thus,

(x, y) = (16, 2)

Please note that it seems your answer choices have not included the correct option.