Question 543968
2x - 7y = 3
5x - 4y =-6
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In the elimination method we multiply one or both equations with values that will
make the coefficient of one of the variables the same but with with different signs
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In the above system, we can multiply the 1st equation by -5 and the 2nd equation by 2, resulting in:
-10x + 35y = -15
+10x - 8y = -12
-----------------adding eliminates x, find y
27y = -27
y = {{{(-27)/27}}}
y = -1
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Use the 1st original equation to find x, replace y with -1
2x - 7(-1) = 3
2x + 7 = 3
2x = 3 - 7
2x = -4
x = {{{(-4)/2}}}
x = -2
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Use the 2nd equation to check our solutions of x=-2 and y=-1
5x - 4y =-6
5(-2) - 4(-1) = -6
-10 + 4 = -6; confirms our solutions
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Has this helped you find your way in the world of eliminations