7.2 by substitution day 1

7.2 Solve Linear Systems by Substitution

P. 435 - 441

• In this section, you will learn the second method to solve a linear system. This method is called SUBSTITUTION.

• This method is not a visual method (like graph-&-check), but a quicker method to find the solution.

Here are the steps to solve using Substitution Method

1. Solve one of the equations for one of its variables. (When possible, solve for a variable that has a coefficient of 1 or -1).

2. Substitute the expression from Step 1 into the OTHER equation and solve the for the other variable.

3. Substitute the value from Step 2 into the revised equation form Step 1 and solve.

EXAMPLE 1 Use the substitution method

Solve the linear system:

y = 3x + 2

Equation 2

Equation 1

x + 2y = 11

Solve for y. Equation 1 is already solved for y.

SOLUTION

STEP 1


Substitute 3x + 2 for y in Equation 2 and solve for x.

7x + 4 = 11 Simplify.

7x = 7 Subtract 4 from each side.

x = 1 Divide each side by 7.

Substitute 3x + 2 for y.x + 2(3x + 2) = 11

Write Equation 2.x + 2y = 11

STEP 2


ANSWER

The solution is (1, 5).

Substitute 1 for x in the original Equation 1 to find the value of y.

y = 3x + 2 = 3(1) + 2 = 3 + 2 = 5

STEP 3

GUIDED PRACTICE

CHECK

y = 3x + 2

5 = 3(1) + 2?

5 = 5

Substitute 1 for x and 5 for y in each of the original equations.

x + 2y = 11

1 + 2 (5) = 11?

11 = 11



Solve the linear system:x – 2y = –6 Equation 1

4x + 6y = 4 Equation 2

SOLUTION

Solve Equation 1 for x.

x – 2y = –6 Write original Equation 1.

x = 2y – 6 Revised Equation 1

STEP 1


Substitute 2y – 6 for x in Equation 2 and solve for y.

4x + 6y = 4 Write Equation 2.

4(2y – 6) + 6y = 4 Substitute 2y – 6 for x.

Distributive property8y – 24 + 6y = 4

14y – 24 = 4 Simplify.

14y = 28 Add 24 to each side.

y = 2 Divide each side by 14.

STEP 2


Substitute 2 for y in the revised Equation 1 to find the value of x.

x = 2y – 6 Revised Equation 1

x = 2(2) – 6 Substitute 2 for y.

x = –2 Simplify.

ANSWER The solution is (–2, 2).

STEP 3

4(–2) + 6 (2) = 4 ?

GUIDED PRACTICE

CHECK

–2 – 2(2) = –6?

–6 = –6

Substitute –2 for x and 2 for y in each of the original equations.

4x + 6y = 4

4 = 4

Equation 1 Equation 2

x – 2y = –6



Solve the linear system using the substitution method.

3x + y = 10

y = 2x + 51.

GUIDED PRACTICE for Examples 1 and 2

ANSWER (1, 7)


x + 2y = –6


x – y = 32.

ANSWER (0, –3)



–2x + 4y = 0


3x + y = –73.


ANSWER (–2, –1)

Assignment: P. 439 3-12

Make sure you have work on your paper to support your answer!! Put answer in an ordered pair (x, y) with parenthesis. Check to see if the ordered pair satisfies both equations!!

7.2 by substitution day 1

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