You can put this solution on YOUR website! we need to get the coefficient of x to be the same.
multiply the first equation through by 2
2x-8y=-46
2x+3y=9
subtract the two equations to eliminate the x
2x-2x-8y-3y=-46-9
-11y=-55
y=-55/-11
y=5
sub this number back into one of the original equations to get your x value
2x-8*5=-46
2x-40=-46
2x=-46+40
2x=-6
x=-3
your solution is x=-3, y=5
You can put this solution on YOUR website! Given the two linear equations:
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X-4Y=-23
2X+3Y=9
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To solve these two equations by elimination we must get the size of one term in the top
equation to be equal to the size of the corresponding term in the bottom equation.
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Let's suppose we decide to eliminate the Y terms in the two given equations. We can do that
by multiplying the entire top equation (all terms on both sides) by 3 to convert it to:
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3X-12Y=-69
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Next let's multiply the entire bottom equation (all terms on both sides) by 4 to convert
it to:
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8X+12Y=36
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So now our two equations are:
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3X-12Y=-69
8X+12Y=36
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Suppose now that we add the two equations vertically in columns. Notice that the 3X and the
8X add to 11X. But more important, notice that in the "Y" column the -12Y and the +12Y
sum to zero because of the difference in their signs. So they disappear. On the right side
the -69 and the +36 sum to -33. So what we are left with if we add the two equations
vertically is:
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11X = -33
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Solve for X by dividing both sides of this equation by 11 (the multiplier of X) to get:
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X = -33/11 = -3
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So we have part of the answer ... X = -3
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Now we can return to either one of the original equations, substitute -3 for X, and solve for
Y. Let's return to X - 4Y = -23. Substitute -3 for X and this equation becomes:
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-3 - 4Y = -23
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Get rid of the -3 on the left side by adding +3 to both sides. When we do the equation becomes:
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-4Y = -20
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Solve for Y by dividing both sides of this by -4 (the multiplier of Y) to get:
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Y = -20/-4 = +5
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So the answer to this problem is X = -3 and Y = +5. This means that the point (-3, 5) is on
the graphs of both given equations.
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Hope this helps you to get the "hang" of finding the common solution for two linear equations
that have a common solution.
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