Answer: x = 2 and y = 0
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Explanation:
We have 3x in the first equation and -3x in the second equation
They add to 0x or simply 0. So the x terms go away when we add them.
Let's add the other corresponding terms.
- The y terms add to -5y+(-8y) = -13y
- The right hand side values add to 6 + (-6) =0
After adding, we have the new equation 0x-13y = 0 or simply -13y = 0. That solves to y = 0 after dividing both sides by -13.
Use this y value to find x.
3x-5y = 6
3x-5(0) = 6
3x = 6
x = 6/3
x = 2
Or you can use the second equation
-3x-8y = -6
-3x-8(0) = -6
-3x = -6
x = -6/(-3)
x = 2
The fact we get the same x value each time helps confirm the answer.
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To fully confirm the answer, you need to plug (x,y) = (2,0) into both equations and simplify. You should get the same number on each side.
Let's check the first equation
3x-5y = 6
3(2) - 5(0) = 6
6 - 0 = 6
6 = 6
That works out. Repeat for the second equation
-3x-8y = -6
-3(2) - 8(0) = -6
-6 - 0 = -6
-6 = -6
That works as well. The answer has been fully confirmed.
Side note: If you graphed the two lines, then they cross at (x,y) = (2,0). This is the x intercept of each line.
