Algebra (SUBSTITUTION METHOD)

Which of the following equations could be the result of using the comparison method to solve the system shown? x - 4y - 1 = 0 x + 5y - 4 = 0

4y + 1 = 4 - 5y

Which of the following equations could be the result of using the comparison method to solve the system shown? x + y = 5 2x + y = 7

5 - x = 7 - 2x

Which of the following equations could be the result of using the comparison method to solve the system shown? x + 2y = 6 x - 4y = 8

6 - 2y = 4y + 8

Which of the following would not be the result of a substitution in the following system? 2x + y = 7 y - x = 1

7 - 2x - x = 1

Solve the following system by the comparison method. 2p + q = 1 9p + 3q + 3 = 0 What is the solution set?

-2,5

Cell Phone Company A charges $20 each month plus $0.03 per text. Cell Phone Company B charges $5 each month plus $0.07 per text. 1. Write a system of equations to model the situation using c for cost and t for number of texts. 2. How many texts does a person need to send in a month to make the costs from both companies equal?

1. 20+0.03t = 5+0.07t 2. two

Solve the following system of equations. 2x + y = 3 x = 2y - 1

2(2y-1)+y=3

For the following system, use the second equation to make a substitution for y in the first equation. 2x + y = 6 y = 3x + 4 What is the resulting equation?

2x + (3x + 4) = 6

Solve the following system of equations by the substitution method. 10x + 10y = 1 x = y - 3 What is the value of y?

31/20

Review

It is difficult to solve a system graphically when the solution does not have integral values. An algebraic solution will allow us to find exact values instead of approximations. The substitution property says that a quantity may be replaced with its equal. In a linear system of equations, substitution results in one equation with one variable. The solution to a linear system is an ordered pair, not just a single value. There may be no solution or an infinite number of solutions. It is important to check the solution to be sure it satisfies the system. There is no one correct way to solve a system of linear equations algebraically. However, you must use the properties correctly.

Steps solve a linear system by substitution:

Solve one of the equations for a variable. Substitute the equivalent expression for the variable in step 1 into the other equation. Solve the resulting equation for the other variable. Substitute that value into the one of the original equations. Solve for the other variable. Check the ordered pair in the other equation. State the solution set.

Based on the lesson, which of the following would be the best approach for solving this system by substitution? 5x = y + 6 2x - 3y = 4

Solve the first equation for y.

substitute

replace a quantity with its equal

Select the best method of finding an accurate solution to a system of linear equations.

use algebraic methods

Solve the following system of equations by the substitution method. 8x = 2y + 5 3x = y + 7 What is the solution set?

{(-9/2, -41/2)}

Solve the following system of equations by the substitution method. x - y = 0 x - y - 2 = 0 What is the solution set?

∅

Shawna and Kai both work at the same pet store. On Monday, Shawna counts 52 birds and cats in the store. For the same animals, Kai counts 138 legs. How many birds and cats are in the pet store?

32 birds and 17 cats

For the following system, use the second equation to make a substitution for x in the first equation. 3x + 2y = 7 x - y + 3 = 0 What is the resulting equation?

3y - 3 + 2y = 7

For the following system, use the second equation to make a substitution for x in the first equation. x + 5y - 10 = 0 x = 2y - 8 What is the resulting equation in simplest form?

7y - 18 = 0

Steps for substitution:

Substitute an equivalent expression for a variable into one of the equations. (We substituted an expression for y.) Solve the resulting equation for the other variable. (We solved for x.) Substitute that value into the one of the original equations. (We put the value of x into one of the equations.) Solve for the other variable. (We solved for y.) Check the ordered pair in the other equation. State the solution set.