SOLUTION: Hello, I am trying to figure out how to solve a system by the method of substitution. I have two problems in which I am having trouble with. 1) {x+3y=8 {y= 2x-9 and

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Hello, I am trying to figure out how to solve a system by the method of substitution. I have two problems in which I am having trouble with. 1) {x+3y=8 {y= 2x-9 and       Log On


   

Question 537186: Hello, I am trying to figure out how to solve a system by the method of substitution. I have two problems in which I am having trouble with.
1) {x+3y=8
{y= 2x-9
and
2) {5x+2y=0
{x-3y=0
I'm confused on how to begin and the proper way to solve the problem, thank you for your help.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
To solve a system of two linear equations by substitution, you solve for one of the variables in one equation and substitute the expression found in the other.
Let's see how it works for your problems.
1) x%2B3y=8
y=+2x-9
Half of the work is already done for you because y=+2x-9 is already "solved" for y, so you just substitute 2x-9 for y in the other equation.
x%2B3%282x-9%29=8
Multiply (apply distributive property)
x%2B6x-27=8
Collect like terms (distributive property backwards, adding apples to apples and x's to x's)
7x-27=8
Add 27 to both sides
7x=8%2B27-->7x=35
Divide both sides by 7
x=5
Then go back to find y
y=2x-9=2%2A5-9=1
So the answer is x=5 with y=1, usually expressed as the pair (5, 1).
2) 5x%2B2y=0
x-3y=0
You need to solve for x or for y one of the two equations I would go with x in the second one:
x-3y=0-->x=3y
Then substitute in the first equation
5%283y%29%2B2y=0-->15y%2B2y=0-->15y=0-->y=0
and then x=3y=3%2A0=0
The solution is (0, 0).