# SOLUTION: 3y-x=2 -2y-x=-18

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 Question 70664This question is from textbook glencoe : 3y-x=2 -2y-x=-18This 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 . 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. . 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. . 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: . +3y - x = +2 +2y + x = +18 ------------- +5y = +20 . 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. . 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: . 3*4 - x = 2 . This becomes: . 12 - x = 2 . Subtracting 12 from both sides results in: . -x = -10 . And finally, we need to solve for +x, so multiply both sides of the equation by -1 to get: . x = 10 . The answers you are looking for are x = 10 and y = 4. . Hope this helps you understand one method of solving a system of two linear equations.