Math 10C

Notes Chapter 7

Section 7.1 Systems of Linear Equations Math 10C

What is this? A system of equations is TWO equations that use the SAME variables.

Why use them? A SOLUTION is the pair of values that make BOTH equations true.

Remember Linear functions come in 3 forms:y = 3x + 52x – 3y = 19

What is a solution?

Is (2, -5) a solution for 2x + y = - 1 and 3x – 2y = 16?

Determine which of the following ordered pair is a solution for the given linear systems of equations.

c = 2d + 2 Solution A c = 4; d = 1c + 2d = -6 Solution B c = -2; d = -2

Setting up Linear Systems:

Tickets are being sold to a school play. Fred bought 3 adult tickets and 2 student tickets for a total of $31.00. Alison bought 1 adult ticket and 1 student ticket for a total of $12.00. Set up a system of equations that represent the data.

a) Define the variables you will be using.

b) Write two equations that model the above situations.

c) If each adult ticket it $7.00, how much is each student ticket?

Sam’s bike shop sells bicycles and tricycles. The total number of wheels in the store is 45. There are 10 more bicycles then there are tricycles.

a. Define the variables you will be using.

b. Write two equations that model the above situations.

c. Is the solution of 15 bicycles and 5 tricycles valid? Show your work.

Homework section 7.1

Section 7.2 Solving Systems Graphically Math 10C

Remember:

Yesterday you learned what a system of equations is, you learned how to translate a word problem into a system of equations as well as how to verify a solution.

TODAY you will learn how to solve the system of equations GRAPHICALLY. Please get out your graphing calculator.

SOLVE means find the INTERSECTION. The solution is the point that is on both lines, and when you graph it, it is the point where the two lines cross.

Solve the linear system x + y = 8 and 3x – 3y = 14

Step 1. In order to use your graphing function, you need to rearrange your equations into the y = mx + b form.

Step 2. Input the first equation into y1 and the second equation into y2

Step 3. Press Graph – do you notice a point where the lines intersect?

Step 4. Determine this point.

2nd TRACE INTERSECT Move the curser to the intersection ENTER ENTER ENTER

Step 5. List the solution as an ordered pair.

You Try: Solve the system x – y = 4 and 2x – 3y = 3

To visit Head-Smashed-In Buffalo Jump, the admission fee is $5.00 for a student and $9.00 for an adult. In one hour, 32 people entered the centre and a total of $180.00 was collected. How many adults visited the centre during this time?

Remember that you will not be able to solve this question right away, you have to work through a procedure. You will need to remember the skills we learned yesterday as well as today to

a. Define your variablesb. Determine your two equations. Make sure they are in y = mx + b form.c. Graph them and find the intersection.d. Verify the solution.

6 pencils and 4 crayons cost $3.40. 3 pencils and 10 crayons cost $4.90. How much does 1 pencil cost?

Homework Section 7.2

Section 7.4 Solving by Substitution Math 10C

What is substitution?

Remember this means to replace any variable with the value equated to that variable.

Given y = x2 – 3x – 1 Solve if x = 3; if x = -1; if x = 2a + 1

Solve the system 3x + 4y = -4 and x + 2y = 2 using substitution

Step 1. Isolate a variable in ONE of the equations.

Step 2. Substitute the value into the unchanged equation.

Step 3. Solve.

Step 4. Replace to solve for the other variable.

Step 5. Verify your solution

You Try. Solve using Substitution 2x – 4y = 74x + y = 5

You Try. Solve using Substitution 2x + y = 5y = -x + 3

Homework from Calendar

Section 7.5 Solving by Elimination Math 10C

Elimination is the last method we will learn for solving systems of equations. Similar to substitution it is an algebraic approach.

x + 2y = 10 x + y = 7

Solve by elimination

You Try

Homework from the Calendar

Section 7.6 Properties of Systems Math 10C

Classify these equations WITHOUT SOLVING

3x + 5y = 9 x + 2y = 6 x + y = 56x + 10y = 8 x + 2y = 2 3x + y = 3

And these as well……

Homework from the Calendar