Solving Systems of Equations

Day 1 (Graphing and Substitution)

2 or more equations with the same set of unknowns

We are doing these

Graphing

Substitution

Elimination

We are doing these today

intersect

Intersect once

Never intersect

Always intersect (same line)

x=3 and y=4,One sol’n at (3, 4)

never intersect, no solution

Parallel lines,Same slope

Yes, divide every term by 2They are the same line

Infinite solutions

5(- y + 5) + 5y = - 5 -5y +25 + 5y = -

5 25 = - 5

NO

No Solution

3x – (4x + 5) = - 15 - x – 5 = -

15 - x = - 10

NO

x = 10

PLUG x=10 IN2y = 4(10) + 52y = 45y = 45/2

NO

2(2y + 1) – 4y = 2 4y + 2 – 4y = 2

2 = 2

INFINITE

Infinite solutions

•Underline important information•Determine variables

M&M bag = m; Hershey bar = h•Set up equationsm + h = 63m + 2h = 16

•Solvem = - h + 6 3m + 2h = 16

3(- h + 6) + 2h = 16- h + 18 = 16

h=2 and m=4

Homework

Solve the following systems of equations. Tell whether each has 1 solution, no or infinite solutions.1. 10x – 2y =6 and y = 5x – 3

2. 2x = y – 3 and 2x + 2y = 213. 2x – 4y = 2 and x = 2y +34. 5x – 7y =0 and y = 2x5. 17 cars and trucks get gasoline at the

gas station. Each car gets 8 gallons. Each truck gets 19 gallons. The station sells 169 gallons. How many cars were there?