I'll do the first three problems to get you started.
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Problem 1
y = -2
4x+6 = -2 ... replace or substitute y with 4x+6
4x = -2-6
4x = -8
x = -8/4
x = -2
Answer: (x,y) = (-2,-2)
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Problem 2
y = -5x-8
3x = -5x-8 .... substitute y with 3x
3x+5x = -8
8x = -8
x = -8/8
x = -1
Use this to find y
y = 3x = 3(-1) = -3
or
y = -5x-8 = -5(-1)-8 = 5-8 = -3
Answer: (x,y) = (-1, -3)
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Problem 3
y = -4x+5
2x-7 = -4x+5
2x+4x = 5+7
6x = 12
x = 12/6
x = 2
Use this to find y
y = -4x+5 = -4(2)+5 = -8+5 = -3
or
y = 2x-7 = 2(2)-7 = 4-7 = -3
Answer: (x,y) = (2, -3)
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Side note:
To check the answers, we plug the coordinates back into the original equations.
For instance, here's what it would look like to check the answer to problem 3.
y = -4x+5
-3 = -4(2)+5 ... plug in (x,y) = (2,-3)
-3 = -8+5
-3 = -3 ... first equation works
y = 2x-7
-3 = 2(2)-7
-3 = 4-7
-3 = -3 ... second equation works
Both equations are true for (x,y) = (2,-3). This verifies the answer to problem 3. The other problems will follow similar steps.
