To solve for systems of equation by graphing, we must graph each equation.
Find the intersection.
To graph each equations, we can do it in three ways.
1. Making tables.
assuming values of x and substitute it to the equation to find y.
3x - 6y = 9
x y
-1 2
1 -1
3 0
When x = -1 , y is 3(-1) - 6y = 9
-3 - 6y = 9
-6y = 9 + 3
-6y = 12
y = -2
When x = 1, y is 3(1) - 6y = 9
3 - 6y = 9
-6y = 9 - 3
-6y = 6
y = -1
When x = 3, y is 3(3) - 6y = 9
9 - 6y = 9
-6y = 9 - 9
-6y = 0
y = 0
x - 2y = 3
x y
-3 -3
1 -1
3 0
When x = -2, y is -3 - 2y = 3
-2y = 3 + 3
-2y = 6
y = -3
When x = 1, y is 1 - 2y = 3
-2y = 3 - 1
-2y = 2
y = -1
When x = 3y is 3 - 2y = 3
-2y = 3 - 3
-2y = 0
y = 0
Then graph each equation
The graph are the same. therefore, the solution are infinite. (many solution)
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