Question 68517
Solution : We can solve these equation in several ways but im going to show you how using Substitution Method.
<br>Here are the Steps 
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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
<br> 
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.
{{{y = -3}}}
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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
{{{x = 2}}}

4. Check the solution in both original equations.
1. x - 2y = 8 , x = 2 and y = -3
   2 - 2(-3) = 8
   8 = 8 ------> True
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2. 3x - 2y = 12 , x = 2 and y = -3
   3(2) - 2(-3) = 12
   6 + 6 = 12
    12 = 12 ----------> True
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Therefore the solution is {{{highlight (x=2)}}} and {{{highlight (y=-3)}}}
<br><br> Graph:
In graphing, you can Make a table, assume values for x and then solve for y. 
x - 2y = 8 
<br> 
 x  |  y
-2  | -5
 0  | -4
 2  | -3
<br> Plot the points (-2, -5),(0, -4), (2, -3) and it should look like the graph below

{{{graph (300, 300, -4, 7, -7, 4, (1/2)x-4)}}}

<br><br> 
2. 3x - 2y = 12 , Assume values of x and then solve for y
<br>
x    |   y
0    |   6
2    |  -3
4    |   0
<br>
{{{graph (300, 300, -4, 7, -7, 4, (3/2)x-6)}}}
 <br>
If we combine the graph it will look like this: 

{{{graph (300, 300, -4, 7, -7, 4, (3/2)x-6, (1/2)x-4)}}}

<br> 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.