Linear Equations

BB-66 : Page 56


and

Graphing the Equations on the Same Graph

1. First thing you have to do is simplify the first equation. After that you should end up with y=5-x .
2. You then have to plot it on a graph. After you've completed that then you put the second equation on the same graph as the first equation.
3. You then continue extending both lines until they intersect each other. They intersect at the point (3, 2). (Refer to Picture 1 at the bottom)

Solving the Problems Algebraically

1. Once you see where they intersect you must then solve for 'y' and 'x' algebraically to ensure that you've got the right coordinates. You have to substitute for 'Y' from the first equation into the second equation.

2. Your equation should look like this:

3. Then you add 'x' to both sides of the equation leaving you with: 5=(1/3)x+1

4. Then you must do additive inverse so you subtract 1 from both sides leaving you with: 4=(1/3)x+x

5. Then you simplify that equation and end up with: 4=(4/3)x

6. To get 'x' by itself, multiply 3/4 to both sides of the equation.

7. You should then end up with x=3

8. To get the 'y' coordinate you must substitute 'x' into one of the two original equations.

9. y=5-3 : 5-3=2 : y=2

10. So you can tell that the lines do cross at the coordinates (3,2)

Picture 1