Question

5x−y=10 3x+y=14 please solve the system of equations and show your work

Answer 1

work is down below. the answers is x=3

Answer 2

x = 3, y = 5

or (3,5) in coordination point form.

Explanation:

We are going to solve the system of equations by combining two equations. To do that, we isolate y-term.

`\large{\begin{cases} 5x - y = 10 \\ 3x + y = 14 \end{cases}}`

Convert both equations to slope-intercept form.

`\large{ \begin{cases} y = 5x - 10 \\ y = - 3x + 14 \end{cases}}`

Then combine both equations

`\large{5x - 10 = - 3x + 14} \\ \large{5x + 3x = 10 + 14} \\ \large{8x = 24} \\ \large{x = 3}`

Substitute x = 3 in one of given equations. I will substitute x = 3 in y = 5x-10

`\large{y = 5x - 10} \\ \large{y = 5(3) - 10} \\ \large{y = 15 - 10} \\ \large{y = 5}`

Hope this helps!