Question

Solve the system of equations. If the system has no solution, say that it is inconsistent. Graph the lines of the system.

X+y=4

{

X-y=2

Answer 1

The solution to the system of the equations will be:

`x=3,\:y=1`

Explanation:

Given the system of the equations

`x+y=4`

`x-y=2`

solving the system of the equations

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

`x-y=2`

`-`

`\underline{x+y=4}`

`-2y=-2`

solving

`-2y=-2`

Divide both sides by -2

`(-2y)/(-2)=(-2)/(-2)`

`y=1`

`\mathrm{For\:}x+y=4\mathrm{\:plug\:in\:}y=1`

`x+1=4`

`x=3`

Therefore, the solution to the system of the equations will be:

`x=3,\:y=1`