Question

I need some step my step notes on how to solve systems of equations like this for example

Answer 1

System of equations:

• Equation 1

`5x+2y=-7`

• Equation 2

`5x+3y=2`

Procedure

This system is easier if we solve it using the elimination method, in which we multiply the first equation times minus one, add both equations to eliminate the x variable, and solve for y.

0. Multiplying Equation 1 times minus 1.

`-1\cdot(5x+2y=-7)`
`-5x-2y=7`

2. Adding both equations:

`\begin{gathered} -5x-2y=7 \\ +(5x+3y=2) \\ --------- \\ 0+1\cdot y=9 \end{gathered}`

Then:

`y=9`

3. Finally, substituting this value in any equation and solving for x:

`5x+2\cdot9=-7`
`5x+18=-7`
`5x=-7-18`
`x=-(25)/(5)=-5`

Answer: y = 9 and x = -5.