1. Warm up
Graph y = 3x – 4
y = -2x + 11
on your graphing calculator.
Look at the table of values. (2nd Table/F5)
Can you find a point that is on both graphs at the same time?

2. 3-1 Solve Systems of Equations
Solve systems of linear equations graphically and algebraically.

3. What is the greatest number of times that two lines can cross
What is the greatest number of times that two lines can cross? What is the least number of times?
To solve a system of linear equations, you are finding the intersection point. This will be the ordered pair that satisfies both equations at the same time.

4. Using a table.
Compare the points from both equations. If they have matching points, you have a solution!

5. One way to solve is to graph both lines and hopefully identify the intersection point from the graph. If the point is on a grid-crossing, life is great, we can try that point into both equations and see if it is true for both. If we have to estimate the fraction or decimal value of x or y, it probably won’t satisfy both equations.
Solve the system of equations by graphing.
4x + 3y = -24
8x – 2y = -16
Classify this system
REMEMBER TO CHECK YOUR SOLUTION!

6. We can also solve a system algebraically
We can also solve a system algebraically. The two methods used are substitution or elimination.

7. 43. Solve each system by using substitution.
9y + 3x = 18
-3y – x = -6
Classify this system
REMEMBER TO CHECK YOUR SOLUTION!

8. 47. Solve by substitution
-9c – 4d = 31
6c + 6d = -24
Classify this system
REMEMBER TO CHECK YOUR SOLUTION!

9. 55. Solve by using elimination
r – 6t = 44
9r + 12t = 0
Classify this system
REMEMBER TO CHECK YOUR SOLUTION!

10. The calculator is helpful for messy answers if you know how to use it.
61. Solve using a graphing calculator. Round coordinates to the nearest hundredth.
5.8x – 6.3y = 18
-4.3x + 8.8y = 32

11. CONCEPT SUMMARY Solving Systems of Equations Method
The Best Time to Use
Table
To estimate the solution, since a table may not give exact solution
Graphing
To estimate the solution, since the graph may not give exact solution
Substitution
If one of the variables in either equation has a coefficient of 1 or -1
Elimination
If one of the variables can be eliminated by either adding equations or multiplying an equation by a constant so that when added a variable is eliminated.
Concept Summary Solving Systems of Equations
Method
The best time to use