4. Solve the following system of equations by

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

and check your answer

a) Graphing

Solve each equation for *y*. For the first one,

first, transpose the *x* term to the other side of the equation.

We do the same thing with the other equation.

but here we also have a coefficient to remove. Divide both sides by -2.

Make up a table of *x*'s and *y*'s for each equation, and graph them both.

and we see that the solution is *x* = -1 and *y* = 3.

if we substitute these numbers into the first equation, we get

which checks.

In the second equation we get

so they check in both equations

Solve one of the equations for one of the unknowns. In this case, it would be best to solve the second equation for *x*.

Substitute this solution into the other equation

This gives us an equation with only one unknown. Solve this equation. First, remove parentheses.

Combine the *y* terms on the left and transpose the -14 to the other side.

or

Divide both sides by 5.

which is what we got the other way.

To find *x*, substitute this solution into the equation where we had solved for *x* as a function of *y*.

and get

or

which is the same solution as we got before.

Multiply the equations by suitable numbers so that the coefficients of the y terms match up. In this case we could simply multiply the top equation by 2.

or

To solve for *y*, substitute this solution into either of the
original equations and solve for *y*. The best equation would be the first
one

or

so all we have to do to solve for y is to add 2 to both sides.