Solve by substitution means you first solve EITHER equation for EITHER x or y. Your choice! So there is no absolute right way to solve this. I was going to start with the second equation, because it didn't have a y, but then I guessed that you probably missed the y? I'm going to solve the following:
3x+2y=-1
2x-7y=4
If the problem is actually as written, you would solve for x in that second equation and go from there.e
I like the first equation, and will solve it for y first:
- 2y=-3x-1 (subtract 3x from both sides)
- y=-3x/2-1/2 (divide both sides by 2)
Now you can substitute this expression for y in the second equation:
- 2x-7(-3x/2-1/2)=4 (direct substitution)
- 2x+21x/2+7/2=4 (distribute the -7)
- 4x+21x+7=8 (multiply everything by 2 to clear the fractions)
- 25x=1 (combine like terms)
- x=1/25
Now you can easily solve for y, using the y= equation:
- y=-3x/2-1/2
- y=-3(1/25)/2-1/2
- y= -3/50-1/2
- y=-14/25
x=1/25, y=-14/25
However...given these answers, I'm wondering if the problem really was as written. If that's the case:
- 2x-7=4
- 2x=11 (+7 both sides)
- x=11/2
- 3(11/2)+2y=-1 (substitute the 11/2 in the first equation)
- 33+4y=-2 (multiply by 2)
- 4y=-35
- y=-35/4
- x=11/2, y=-35/4 (these answers aren't pretty either)
