3. Solve the following system of equations by

and check your answer.

a) Graphing

Solve the first equation for   y.

2y = -3x + 6

Solve the second equation for   y.

3x - 3 = y

Graph both equations,

and we see that the point where the lines meet does not have both of its coordinates whole numbers, so we will need to use a more computational method to get the solution.

b) Substitution

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Solve one of the equations for one of the unknowns. The simplest unknown would be the x in the first equation. Solve the second equation equation for   y.

y = 3x - 3

Substitute this in for   y   in the other equation.

3x + 2(3x - 3) = 6

This gives us an equation in only one unknown. Solve this equation.

3x + 6x - 6 = 6

9x - 6 = 6

9x = 12

x = 12/9 = 4/3

The simplest way to find   y   is to substitute this solution into the equation where we expressed   y   as a function of   x.

y = 4 - 3

y = 1

So the solution is   x = 4/3,   y = 1.

Check: In the first equation,

4 + 2 = 6

and it checks. For the second equation,

4 - 1 = 3

and the solution checks in both equations.

c) Addition

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We are very lucky here. The coefficients on the x's already match up. We need only subtract the bottom equation from the top.

            3y = 3

Divide both sides by 3.

              y = 1

To find   x,   substitute this into an equation which has an   x.

3x + 2(1) = 6

3x + 2 = 6

Subtract 2 from both sides of the equation.

3x = 4

Divide both sides by 3.

x = 4/3

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