Solve the system: -3x + 2y = 23 and 5x + 2y = -17

1/19/2021

How do you solve this system of equations?
-3x + 2y = 23
5x + 2y = -17

One way to solve this system, is to subtract the two equations as they are. This would eliminate the y,
and then you can solve for x.

-3x + 2y = 23
5x + 2y = -17
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-8x = 40 {subtracted the two equations}
x = -5 {divided each side by -8}

-3x + 2y = 23 {first equation}
-3(-5) + 2y = 23 {substituted 5, in for x, into first equation}
15 + 2y = 23 {multiplied -3 by -5}
2y = 8 {subtracted 15 from each side}
y = 4 {divided each side by 2}

x = -5 and y = 4

If you graph the two equations on a graphing calculator,
that is the point of intersection of the two lines.