3x-2y=0
x+y=-5
We are almost ready for substitution; we just have to get one variable alone. Since x + y = -5, then x = -5 - y.
Substitute this into the first equation and you have
3(-5 - y) - 2y = 0
Distribute
-15 - 3y - 2y = 0
Combine like terms
-15 - 5y = 0
-5y = 15
y = -3
Now plug back into the expression you substituted to find x:
x = -5 - y ...so... x = -5 - -3 ... x = -5+3 ... x = -2
Now double-check the first equation (we know the second equation works) with the values we found:
3(-2) - 2(-3) = 0
-6 - -6 = 0
-6 + 6 = 0
CHA-CHING!
===============
3x-2y=0
x+y=-5
To solve with elimination, double the second equation (the -2y and the positive y are just aching to be eliminated):
3x - 2y = 0
2x + 2y = -10
Add 'em up:
5x = -10
So x = -2, you plug it into any equation to find y, check your answer, and
CHA-CHING!
=====================
4x+2y=8
y=-2x+4
This one's all set for substitution. Take the second equation (already solved for y) and plug it into the first equation:
4x + 2(-2x + 4) = 8
4x + -4x + 8 = 8
4x - 4x = 0
4x = 4x
x = x
OH SNAP! Any x value will work, so there are INFINITELY MANY SOLUTIONS.
=========
If we try elimination (but who would? substitution was all set up for us), we need the equation to line up
4x+2y=8
y=-2x+4
Add 2x to both sides of the second equation so that all the variables are on the left side:
4x + 2y = 8
2x + y = 4
Now let's double the second equation
4x + 2y = 8
4x + 2y = 8
OH SNAP! Same equation, so really we just have one equation, and there are infinitely many solutions.
We’ll help your grades soar
Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.
- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support
Already a member? Log in here.
Are you a teacher? Sign up now