Unit One

Key Concepts

- to solve a system of two linear equations means to find the point of intersection of the two lines

- check an answer by substituting it into the two original equations (equal answers means that it is right)

- you can solve linear systems by graphing, using substitution, or elimination

STEPS TO SOLVE BY SUBSTITUTION

1: Solve one of the equations for one variable in terms of the other variable.

2: Substitute the expression from step 1 into the other equation and solve for the remaining variable.

3: Substitute back into one of the original equations to find then value of the other variable.

4: Check the solution by substituting into both original equations.

STEPS TO SOLVE BY ELIMINATION

1: Arrange equations so like terms are aligned.

2: Choose the variable you wish to eliminate.

3: If necessary, multiply one or both equations by a value so that they have the same or opposite coefficient in front of the variable you want to eliminate.

4: Add or subtract (as needed) to eliminate one variable.

5: Solve for the remaining variable. Substitute into one of the original equations to find the value fo the other variable.

6: Check solution by substituting into original equations.

TYPES OF QUESTIONS

Distance, Speed, Time

A canoeist took 2 h to travel 12 km down a river. The return trip, against the current, took 3 h. What was the average paddling rate of the canoeist? What was the speed of the current? (pg 44)

Direction

Distance (km)

Speed (km/h)

Time (h)

Downstream

12

P + c

2

Upstream

12

P – c

3

Mixture Problems

Mariam has a bottle of 5% acetic acid and a bottle of 10% acetic acid. How much of each should she use to make 250 mL of 8% acetic acid? (pg 45)

Volume (mL)

5% Acid

10% Acid

8% Mixture

Solution

F

T

250

Pure Acid

0.05 f

0.1 t

0.08 (250)

	Created by liyana45 over 10 years ago

High School Diploma Math Note on Unit One- Linear Systems, created by liyana45 on 21/12/2013.