How do you solve the system #2x - 5y = 5# and #2x + 2y = 26#?
We subtract the left side of equation 2 from the left side of equation 1, and the right side of equation 2 from the right side of equation 1. See explanation.
General Method: For a more general solution for this type of problem, consider:
To perform the operation here, we must combine the two rows in some manner that only gets rid of one variable. Supposing we wish to remove the x variable by subtracting some multiple of the second equation from the first, we would multiply the left and right hand sides of equation 2 by
Divide by the coefficient of the y term on both sides:
Having found y, we would plug it into either equation to find x.
Solution to this specific problem:Because our coefficient on the x terms for both equations is the same (i.e. 2), the first thing we can do is simply subtract the second equation from the first. We do this as follows:
Substitute this back into our first or second equation (we will use first here):
Thus our solution is
Plug this into each equation to check your work.
Thus our solution of