Question 68517: solve each equation and graph
x - 2y = 8
3x - 2y = 12
Found 2 solutions by checkley71, rmromero:
Answer by checkley71(8403)   (Show Source):
You can put this solution on YOUR website! X-2Y=8
X=2Y+8 NOW SUBSTITUTE (2Y+8) FOR X IN THE OTHER EQUATION
3(2Y+8)-2Y=12
6Y+24-2Y=12
4Y=12-24
4Y=-12
Y=-12/4
Y=-3 SOLUTION NOW SUBSTITUTE -3 FOR Y & SOLVE FOR X
X-2*-3=8
X+6=8
X=8-6
X=2 SOLUTION
 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions y = x/2 -4 and y = 3x/2 -6).
Answer by rmromero(383) (Show Source):
You can put this solution on YOUR website! Solution : We can solve these equation in several ways but im going to show you how using Substitution Method.
Here are the Steps
1. In either equation, solve for one variable in terms of the other. I am going to choose simple equation for this.
x - 2y = 8 , Solve x in terms of y
x = 2y +8
2. Substitute 2y + 8 for x in the other equation 3x - 2y = 12. Solve for y.
3(2y +8) - 2y = 12 , Use Distributive Property to simplyfy this.
6y + 24 - 2y = 12 , Combine like terms.
4y = -12 , Divide both sides by 4 to solve for y.
3. Substitute the result from step 2 in either equation. Solve for the other variable. You can use either of the two equation.
x - 2y = 8 , y = -3
x - 2(-3) = 8
x + 6 = 8
4. Check the solution in both original equations.
1. x - 2y = 8 , x = 2 and y = -3
2 - 2(-3) = 8
8 = 8 ------> True
2. 3x - 2y = 12 , x = 2 and y = -3
3(2) - 2(-3) = 12
6 + 6 = 12
12 = 12 ----------> True
Therefore the solution is  and 
Graph:
In graphing, you can Make a table, assume values for x and then solve for y.
x - 2y = 8
x | y
-2 | -5
0 | -4
2 | -3
Plot the points (-2, -5),(0, -4), (2, -3) and it should look like the graph below
2. 3x - 2y = 12 , Assume values of x and then solve for y
x | y
0 | 6
2 | -3
4 | 0
If we combine the graph it will look like this:
The green line is the graph of x - 2y = 8 and the red one is the graph of 3x - 2y = 12. The solution x = 2 and y = -3 means that the lines intersect at that point.
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