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solve each linear system by GRAPHING. CHECK YOUR ANSWER
2.) x - y = 6
2x = 12 + 2y

3.)1/2 x - y = 4
2y = x + 6

Sagot :

Answer:

2.) Infinitely many solutions

3.) No solutions

Step-by-step explanation:

To solve systems of equations graphically, you need to find where they intersect

2.) First put each equation in the form y=mx+b

x-y=6 -> y= x-6

2x=12+2y -> y= x-6

Then, graph each line

Since we have the same equation, the lines are on top of each other so there are infinitely many solutions as they intersect everywhere.

To check, plug a point in from the graph into both equations and you should get 0=0

3.) First put each equation in the form y=mx+b

1/2x-y=4 -> y=1/2x-4

2y=x+6 -> y=1/2x+3

Then, graph each line

Since the lines have the same slope but a different y intercept, the lines are parallel. Therefore, there are no solutions as they do not intersect.

To check your answer, you would one equation as the y in the other equation.

2(1/2x-4)=x+6, then solve for x

Then plug that x into the original equations, and you'll see they are not equal. Hope that helps!

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