Answer: (x,y) = (6,-3)
This means 6 goes in the first blank and -3 goes in the second blank.
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Explanation:
Solve the second equation for x
x+8y = -18
x = -18-8y
We'll plug that into the first equation and isolate y. This is where substitution comes in.
5x + 7y = 9
5( x ) + 7y = 9
5( -18-8y ) + 7y = 9 ... replace x with -18-8y
-90-40y + 7y = 9
-90-33y = 9
-33y = 9+90
-33y = 99
y = 99/(-33)
y = -3
Use this y value to find x
x = -18-8y
x = -18-8(-3)
x = -18+24
x = 6
The solution is (x,y) = (6,-3)
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Checking the answer:
Let's check the first equation
5x+7y = 9
5(6)+7(-3) = 9 ... plug in (x,y) = (6,-3)
30-21 = 9
9 = 9 .... true equation
Do the same for the second equation as well
x+8y = -18
6 + 8(-3) = -18
6 - 24 = -18
-18 = -18 .... also true
Both equations are true when we plug in (x,y) = (6,-3), so the solution is confirmed.
