Answer: (x, y) = (-9, 7)
In other words, x = -9 and y = 7 pair up together to form the solution.
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Step-by-step explanation:
Add the equations straight down
- The x terms cancel out since 7x+(-7x) = 0x = 0
- The y terms add to -3y because 5y+(-8y) = -3y
- The right hand sides add to -28+7 = -21
We end up with -3y = -21 which solves to y = 7. I divided both sides by -3.
Then use this value of y to find x.
7x+5y = -28
7x+5(7) = -28
7x+35 = -28
7x = -28-35
7x = -63
x = -63/7
x = -9
Or you could say
-7x-8y = 7
-7x-8(7) = 7
-7x - 56 = 7
-7x = 7+56
-7x = 63
x = 63/(-7)
x = -9
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In summary we found that x = -9 and y = 7 pair up together.
The ordered pair solution is (x, y) = (-9, 7)
To verify this answer, plug those coordinates into each of the original equations. You should get the same thing on both sides when you simplify fully. I'll let you do this verification.
A visual way to check the answer is to graph the equations on the same xy grid. The two lines intersect at (-9, 7)
GeoGebra and Desmos are two graphing apps I recommend. Both are free.