Systems Study Guide

Systems Study Guide

1) Substitution

2) Elimination

3) Graphing with Intercepts

4) Word Problem Set Up

Substitution

1) manipulate 1 equation to be isolated

2) substitute into other equation and solve

3) back-substitute to find remaining variable

Multiple Choice

Practice solving the system by SUBSTITUTION:

-5x + y = -2

-3x + 6y = -12

• (-2,0)

• (0,-2)

• (2,0)

• (-2,0)

ELIMINATION

1) multipliers to both top and bottom to create opposites

2) add the 2 equations and solve

3) back-substitute to find remaining variable

Multiple Choice

Practice solving the system by ELIMINATION:

-5x + 2y = 32

2x + 3y = 10

• (-4,6)

• (14,-6)

• (2,2)

• (-2,11)

GRAPHING (USING INTERCEPTS)

1) plot the x and y intercepts for the first equation

2) plot the x and y intercepts for the second equation

3) find point of intersection

Multiple Choice

Practice solving system by GRAPHING:

2x + y = 2

2x - 3y = 18

• no solution

• (-4,3)

• (3,-4)

• (4,-6)

SET UP FOR WORD PROBLEM

1) generic totals: x + y = total

2) money totals: #x + #y = $total

Multiple Choice

Tickets for a Valentine's Dance cost $3 for individuals or $5 for couples. 180 tickets were sold and $475 collected. Set up a system.

• x + y = 475

  3x + 5y = 180

• 3x + 5y = 475

  x + y = 180

• 3x + 5y = 180

  3x + 5y = 475

• 3x + 5x = 180

  3y + 5y = 475