Question

Solve this system.2x – y=1-3x + y = -5

Answer 1

Hello there. To solve this question, we'll have to remember some properties about system of equations.

Given the system:

`\begin{cases}2x-y=1 \\ -3x+y=-5\end{cases}`

We'll solve it by the addition method. Notice in the first equation we have - y, while we have a + y on the second equation.

Adding both equations, we have:

`\begin{gathered} 2x-y-3x+y=1-5 \\ -x=-4 \end{gathered}`

Multiply both sides of the equation by a factor of (-1)

`x=4`

Plugging this value in any of the two equations, we get:

`\begin{gathered} 2\cdot4-y=1 \\ 8-y=1 \end{gathered}`

Add y - 1 on both sides of the equation

`\begin{gathered} 8-y+y-1=1+y-1 \\ y=7 \end{gathered}`

Therefore the ordered pair that is solution for this system of equation is:

`(x,y)=(4,7)`