3. Solve the following system of equations by

- a) Graphing
- b) Substitution
- c) Addition

and check your answer.

a) Graphing

Solve the first equation for *y*.

2*y* = -3*x* + 6

Solve the second equation for *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.

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.*

Substitute this in for *y* in the other equation.

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

9*x* - 6 = 6

9*x* = 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

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.

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

3*y* = 3

Divide both sides by 3.

*y* = 1

3*x* + 2(1) = 6

3*x* + 2 = 6

Subtract 2 from both sides of the equation.

3*x* = 4

Divide both sides by 3.