# Thread: Solving equations - to Graph!

1. ## Solving equations - to Graph!

How do you solve these corresponding equations (will use the values of y and x to graph)

3x-y-=5 and x+3y=6

I've figured out how to solve 3x-y=5 by doing this:
3x-y=5
y=3x-5

But what about the other one? (x+3y=6)

2. Originally Posted by cnmath16
How do you solve these corresponding equations (will use the values of y and x to graph)

3x-y-=5 and x+3y=6

I've figured out how to solve 3x-y=5 by doing this:
3x-y=5
y=3x-5

But what about the other one? (x+3y=6)
Solve the second equation for y:

$x+3y=6~\implies~3y=-x+6~\implies~y=-\dfrac13 x + 2$

Now draw the graphs of these equations. The coordinates of the intersection point are the solutions of both equations.

According to my sketch I got x = 2.1 and y = 1.3

3. Originally Posted by cnmath16
How do you solve these corresponding equations (will use the values of y and x to graph)

3x-y-=5 and x+3y=6

I've figured out how to solve 3x-y=5 by doing this:
3x-y=5
y=3x-5

But what about the other one? (x+3y=6)
this here is a common linear system.
there are three ways to solve, elimination, substitution, and by graphing

I will use substitution since it is easiest for this linear system

y=3x-5
x+3y=6
plug the value of y into the second equation

x+3(3x-5)=6
x+9x-15=6
10x=6+15
x=21/10
x=2.1

take that value and plug it into the other equation

y=3(2.1)-5
y=6.3-5
y=1.3

Thefore, the answer is (2.1,1.3)