3. Solve the following system of equations by

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

top

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.

top

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