Solving Systems of Linear Equations by Substitution Essential Question? How can you solve a system of equations by substitution? 8.EE.8b

Common Core Standard: 8.EE.8 ─ Analyze and solve linear equations and pairs of simultaneous linear equations. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6..

Objectives: To solve a system of linear equations using substitution.

Example:

ACCURACY Using a graph to determine the solution of a linear system gives us an ESTIMATE We need a more accurate way of determining a solution when the graphs don’t match perfectly with the grid lines

METHODS Graphing (only gives an ESTIMATE) Substitution Elimination (also called linear combinations)

they are equal to each other! Time to think! If two things are equal to the same thing they are equal to each other! y = 5x + 2 y = 3x - 7 Since both expressions (5x + 2) and (3x - 7) are equal to y, they are equal to each other! 5x + 2 = 3x - 7

SUBSTITUTE it in another equation. SUBSTITUTION If you know what one thing equals, you can SUBSTITUTE it in another equation. EXAMPLE: Since y = 2x - 1, we can substitute the expression (2x - 1) everywhere we see the letter y.

Solution is (2, 4) Check!

INTERPRETATION The SOLUTION is the POINT OF INTERSECTION of the two lines. It is the place where the two lines cross. Lines that INTERSECT have ONE SOLUTION.

Graphic Method Substitution

Solve using substitution. Check!

Solve using substitution. Check!

Solve using substitution.

Chatty Phone charges a flat monthly fee of $20 plus 8 c a minute. Telco charges $14 plus 10 c a minute. When do they charge the same? Let x = # of minutes Let y = total cost Chatty Telco At 300 min. they charge the same.