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3-2: Solving Systems of Equations using Substitution. Solving Systems of Equations using Substitution. Steps: 1. Solve one equation for one variable ( y = ; x = ; a =) 2. Substitute the expression from step one into the other equation.

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Solving systems of equations using substitution l.jpg
Solving Systems of Equations using Substitution

Steps:

1. Solve one equation for one variable (y= ; x= ; a=)

2. Substitute the expression from step one into the other equation.

3. Simplify and solve the equation.

4. Substitute back into either original equation to find

the value of the other variable.

5. Check the solution in both equations of the system.


Example 1 l.jpg
Example #1:

y = 4x

3x + y = -21

Step 1:Solve one equation for one variable.

y = 4x(This equation is already solved for y.)

Step 2: Substitute the expression from step one into the other equation.

3x + y = -21

3x + 4x = -21

Step 3: Simplify and solve the equation.

7x = -21

x = -3


Slide4 l.jpg

y = 4x

3x + y = -21

Step 4: Substitute back into either original

equation to find the value of the other

variable.

3x + y = -21

3(-3) + y = -21

-9 + y = -21

y = -12

Solution to the system is (-3, -12).


Slide5 l.jpg

y = 4x

3x + y = -21

Step 5: Check the solution in both equations.

Solution to the system is (-3,-12).

3x + y = -21

3(-3) + (-12) = -21

-9 + (-12) = -21

-21= -21

y = 4x

-12 = 4(-3)

-12 = -12


Example 2 l.jpg
Example #2:

x + y = 10

5x – y = 2

Step 1: Solve one equation for one variable.

x + y = 10

y = -x +10

Step 2: Substitute the expression from step one into

the other equation.

5x - y = 2

5x -(-x +10) = 2


Slide7 l.jpg

x + y = 10

5x – y = 2

Step 3: Simplify and solve the equation.

5x -(-x + 10) = 2

5x + x -10 = 2

6x -10 = 2

6x = 12

x = 2


Slide8 l.jpg

x + y = 10

5x – y = 2

Step 4: Substitute back into either original

equation to find the value of the other

variable.

x + y = 10

2 + y = 10

y = 8

Solution to the system is (2,8).


Slide9 l.jpg

x + y = 10

5x – y = 2

Step 5: Check the solution in both equations.

Solution to the system is (2, 8).

5x – y = 2

5(2) - (8) = 2

10 – 8 = 2

2 = 2

x + y =10

2 + 8 =10

10 =10



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