Answer: (x,y) = (2,-2)
This means x = 2 and y = -2
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Step-by-step explanation:
Let's solve the first equation for y
5x+y = 8
y = 8-5x
Then we'll plug this into the second equation
-3x + 2y = -10
-3x + 2( y ) = -10
-3x + 2(8-5x) = -10
-3x + 16 - 10x = -10
-13x + 16 = -10
-13x = -10-16
-13x = -26
x = -26/(-13)
x = 2
Use this value to find y
y = 8-5x
y = 8-5(2)
y = 8-10
y = -2
The ordered pair solution is (x,y) = (2,-2)
This is where the two lines cross.
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To check the answer, plug the x and y coordinates into each equation. We should get the same number on both sides of each equation.
For the first equation, we have:
5x+y = 8
5(2)-2 = 8
10-2 = 8
8 = 8
That works. Repeat for the second equation
-3x+2y = -10
-3(2)+2(-2) = -10
-6 - 4 = -10
-10 = -10
That checks out as well. Both equations are true when x = 2 and y = -2. The answer is confirmed.