SOLUTION: Use elimination method to find all solutions of the system of equations. 8x+4y-112 40x+2y=380

Question 529563: Use elimination method to find all solutions of the system of equations.
8x+4y-112
40x+2y=380
Answer by lmeeks54(111) (Show Source): You can put this solution on YOUR website!
With n # of equations and n # of unknowns, the elimination method is useful in solving the system of equations, one unknown at a time. That is, with two equations such as we have here, we can re-cast one of the equations in terms of one of the unknowns, then plug that equality into the other equation so you then have one equation with one unknown. Solve for that unknown, then substitute that value back into one of the original equations to solve for the other unknown.
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8x + 4y = 112
40x + 2y = 380
...
Let's work on the 1st equation first (but it doesn't matter the order):
8x + 4y = 112
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subtract 8x from both sides:
4y = 112 - 8x
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divide both sides by 4:
y = 28 - 2x
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take the value for y, in terms of x, and insert it into the other original equation:
40x + 2y = 380
40x + 2(28 - 2x) = 380
40x + 56 - 4x = 380
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subtract 56 from both sides and simplify:
36x = 324
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divide both sides by 36:
x = 9
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go back to our equation where have y in terms of x and solve for y:
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y = 28 - 2x
y = 28 - 2(9)
y = 10
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check our work by substituting x = 9 and y = 10 both original equations:
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8(9) + 4(10) = 112
72 + 40 = 112
112 = 112 checks
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40x + 2y = 380
40(9) = 2(10) = 380
360 + 20 = 380
380 = 380 checks
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the solution to our system of equations is:
x = 9
y = 10
...
cheers,
Lee
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