Question 70664This question is from textbook glencoe
: 3y-x=2
-2y-x=-18
This question is from textbook glencoe
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! +3y - x = 2
-2y - x = -18
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One of the ways to solve this system of equations is to eliminate one of the variables
and solve the resulting equation for the other variable.
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In the above problem you can notice that there is a -x in the top equation and a -x in the
bottom equation. If you subtract the bottom equation from the top equation, the equation
that results does not contain an x. Remember the algebraic rule for subtracting ... change
the signs of the subtrahend (number being subtracted) and add the result to the number that
the subtrahend is being subtracted from.
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To follow this rule we change the sign of -2y so that it becomes +2y. We also change the
sign of the -x so that it becomes +x. And finally, we change the sign of the -18 to +18.
Then we add these terms to the terms directly above them. In algebrais form this becomes:
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+3y - x = +2
+2y + x = +18
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+5y = +20
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The expression below the dashed line is a new equation resulting from the addition.
You can solve this new equation for y by dividing both sides by 5 to get y = 4.
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Next take that value for y and plug it into either of the original two equations and solve
for x. For example, if we substitute 4 for y in the equation 3y - x = 2, we get:
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3*4 - x = 2
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This becomes:
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12 - x = 2
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Subtracting 12 from both sides results in:
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-x = -10
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And finally, we need to solve for +x, so multiply both sides of the equation by -1 to get:
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x = 10
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The answers you are looking for are x = 10 and y = 4.
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Hope this helps you understand one method of solving a system of two linear equations.
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