Question

Find the solution set of the following equations:

2y=2x+7

X=y+2

Answer 1

The system of equations has no solution.

Explanation:

Given the system of equations

2y = 2x+7

x = y+2

solving the system of equations

`\begin{bmatrix}2y=2x+7\\ x=y+2\end{bmatrix}`

Arrange equation variables for elimination

`\begin{bmatrix}2y-2x=7\\ -y+x=2\end{bmatrix}`

Multiply -y+x=2 by 2: -2y+2x=4

`\begin{bmatrix}2y-2x=7\\ -2y+2x=4\end{bmatrix}`

so adding

`-2y+2x=4`

`+`

`\underline{2y-2x=7}`

`0=11`

so the system of equations becomes

`\begin{bmatrix}2y-2x=7\\ 0=11\end{bmatrix}`

0 = 11 is false, therefore the system of equations has no solution.

Thus,

No Solution!