Expert: John Zalewski - 1/4/2006

Question
-3x+y=-3    5x-2y=10



i need help in substitution please help

Answer
Hello, Addy.

To solve this problem, you need to first solve for either
'x' or 'y' in one of the equations.

I chose to solve for y in the equation on the left, but you may choose to solve for either x or y in either equation.

y = -3 + 3x (add 3x to both sides).

This is what y is equal to in the equation on the left.
y = -3 + 3x. Now, since we know what y equals, we can substitute (-3 + 3x) into the equation on the right for y.


5x - 2(-3 + 3x) = 10 (substitute -3+3x for y in the equation on the right side).

5x + 6 - 6x = 10 (multiply the -2 through the parentheses).

-x = 4 (combine the x terms; subtract 6 on both sides).

x = -4 (multiply by -1).

Now you know what x is equal to. x = -4. Now, plug -4 into either equation for x, and solve for y.


-3(-4) + y = -3 (plug in -4 for x in the equation on the left side).

12 + y = -3 (multiply -3 and -4).

y = -15 (subtract 12 from both sides).

Therefore, x = -4, and y = -15. (The calculation below shows a check for the entire problem. By plugging in values for x and y (-4 and -15) in either equation, the answers should work out. I only checked my answers with the equation on the right.)

5(-4) - 2(-15) = 10

-20 + 30 = 10


Hope this helps. If you have any further questions about this or anything else, please do not hesitate to ask.

Regards,
John