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please help answer this systems of equations: substitution and elimination method , please show all work.
y = -4x-8
-8x-4y = -8
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1. Substitution method
y = -4x - 8 (1)
-8x - 4y = -8 (2)
You just have y expressed via x in the equation (1).
So, simply substitute this expression for y into the equation (2).
You will get a single equation for x:
-8x - 4*(-4x - 8) = -8. (3)
Simplify and solve it:
-8x +16x + 32 = -8,
8x + 32 = -8,
8x = -8 - 32,
8x = -40,
x = = .
Then, according to (1), y = -4x - 8 = -4*(-5) - 8 = 20 - 8 = 12.
Answer. x = -5, y = 12.
2. Elimination method
Rewrite your original system in an equivalent form
4x + y = -8 (1')
-8x - 4y = -8 (2')
Now multiply the equation (1') by 2 and add to the equation (2').
In this way you eliminate the unknown x and get a single equation for the unknown y:
2y - 4y = -16 - 8.
Simplify it:
-2y = -24,
y = = 12.
Then from (1') 4x = -8 -y = -8 - 12 = -20 and x = = -5.
Thus you got the same answer.