Dr. Fowler CCM Solving Systems of Equations By Substitution – Harder.

Dr. Fowler CCM

Solving Systems of EquationsBy Substitution – Harder

Solving a system of equations by substitution

Step 1: Solve an equation for one variable.

Step 2: Substitute

Step 3: Solve the equation.

Step 4: Plug back in to find the other variable.

Step 5: Check your solution.

Pick the easier equation. The goal

is to get y= ; x= ; a= ; etc.

Put the equation solved in Step 1

into the other equation.

Get the variable by itself.

Substitute the value of the variable

into the equation.

Substitute your ordered pair into

BOTH equations.

ALREADY IN NOTES – Read Only for Review

1) Solve the system using substitution

3y + x = 7

4x – 2y = 0

Step 1: Solve an equation for one variable.

Step 2: Substitute

It is easiest to solve the

first equation for x.

3y + x = 7

-3y -3y

x = -3y + 7

4x – 2y = 0

4(-3y + 7) – 2y = 0

3y + x = 7

4x – 2y = 0

Step 4: Plug back in to find the other variable.

4x – 2y = 0

4x – 2(2) = 0

4x – 4 = 0

4x = 4

x = 1

Step 3: Solve the equation.

-12y + 28 – 2y = 0-14y + 28 = 0

-14y = -28y = 2

1) Solve the system using substitution

3y + x = 7

4x – 2y = 0

Step 5: Check your solution.

(1, 2)3(2) + (1) = 7

4(1) – 2(2) = 0

1) Solve the system using substitution

Answer is (1,2)

2) Solve the following system using the substitution method.3x – y = 6 and – 4x + 2y = –8

STEP 1 – Solve the first equation for y is easiest, 3x – y = 6

–y = –3x + 6 (subtract 3x from both sides) y = 3x – 6 (multiply both sides by – 1)

STEP 2 – Substitute this value for y in the OTHER equation. –4x + 2y = –8 –4x + 2(3x – 6) = –8 (replace y to other equation) –4x + 6x – 12 = –8 (use the distributive property)

2x – 12 = –8 (simplify the left side) 2x = 4 (add 12 to both sides)

x = 2 (divide both sides by 2)

CONTINUED >

STEP 3 – To get y, substitute x = 2 into either original equation. The easiest is the one that was already solved for y.

y = 3x – 6 = 3(2) – 6 = 6 – 6 = 0y = 0

We have now found x & y. Answer is (2, 0)

EXAMPLE 3

TRUE – The answer is infinitely many solutions

Solve the system by the substitution method.3 7

4 12 28

x y

x y

Solve first for x:3 33 7y yx y

7 3x y 4 127 3 28yy 28 12 12 28y y

28 28

Substitute:

EXAMPLE 4

411 1x y

Use substitution to solve the system.

4 1x y 2 14 5 11 yy

28 1 22 5 1y y

13 1

1

3

13 3y

1y

3, 1

4 11x

1 4

2 5 11

x y

x y

4 1x 3x

Solve first for x:

Substitute into other equation:

To get X, substitute y you found into equation already solved for X:

Example #5: x + y = 10 5x – y = 2

Step 1: Solve one equation for one variable.

x + y = 10

y = -x +10

Step 2: Substitute into the other equation.

5x - y = 2

5x -(-x +10) = 2

x + y = 10 5x – y = 2

5x -(-x + 10) = 2

5x + x -10 = 2

6x -10 = 2

6x = 12

x = 2

Step 3: Simplify and solve the equation.

x + y = 10 5x – y = 2

Step 4: Substitute back into either original equation to find the value of the other variable.

x + y = 102 + y = 10 y = 8

Solution to the system is (2,8).

Excellent Job !!!Well Done

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