Question

Find the solution set of the following equations:

2y=2x+7

X=y+2

Answer 1

Answer:

The system of equations has no solution.

Step-by-step 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!