# Math 3

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If you want to be eligible for partial credit, please show your work.

Solve the following system of equations using any method.

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

Try substituting the equations.

if y=1/3x-2, then

1/3x-2 = 1/2x+3

Solve for x, then plug your solution in for y

Does x=4 and y=2

No. It's going to be tricky dealing with the fractions. Get all of your x terms on one side and your "regular" numbers on the other side.

CAn you give me x so that I can find y?
Cause I did it and got x=3.4

Me too.Are you Danny from Mrs.Pfeiffer's 4th period?Oh Danny!I know you!Yeah AMy help him too,we are both in the same class.

Set the two equations equal to each other.

1/2x + 3 = 1/3x - 2 (If both are equal to y, they must be equal to each other.)

Condense the x's and the whole numbers to different sides. You will have to find the least common denominator:

1/2x - 1/3x = -3 -2
3/6x - 2/6x = -5
1/6x = -5

To solve, multiply each side by 6 (the reciprocal of 1/6)

You should get x = 30

Does that make sense?

Yes,thank you!So then does y=23

If y= 1/3x - 2, then plug in x.

If x = -30, then

y = 1/3 (-30) - 2
y = -10 - 2
y = -12

Try plugging in x in the second equation. Both y's should be equal.

Write one or two equations to represent the situation below. Solve the equation(s). Show all your work.

Two cars leave town going in opposite directions. The car heading north travels at 55 mph. The car heading south travels at 75 mph. How long will it take them to get 715 miles apart?