Solve Systems of Equations Using Elimination Section 6.3

Solve Systems of Equations Using

Elimination

Section 6.3

Solving Systems of Equations

So far, we have solved systems using graphing and substitution. These notes show how to solve the system algebraically using ELIMINATION with addition and subtraction.

Elimination is easiest when the equations are in standard form.

Solving a system of equations by elimination using addition and subtraction.

Step 1: Put the equations in Standard Form.

Step 2: Determine which variable to eliminate.

Step 3: Add or subtract the equations.

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

Step 5: Check your solution.

Standard Form: Ax + By = C

Look for variables that have thesame coefficient.

Solve for the variable.

Substitute the value of the variableinto the equation.

Substitute your ordered pair intoBOTH equations.

1) Solve the system using elimination.

x + y = 53x – y = 7

2) Solve the system using elimination.

4x + y = 74x – 2y = -2

Which step would eliminate a variable?

3x + y = 43x + 4y = 6

1. Isolate y in the first equation

2. Add the equations3. Subtract the equations4. Multiply the first

equation by -4

Solve using elimination.

2x – 3y = -2x + 3y = 17

1. (2, 2)2. (9, 3)3. (4, 5)4. (5, 4)

3) Solve the system using elimination.

y = 7 – 2x4x + y = 5

What is the first step when solving with elimination?

1. Add or subtract the equations.2. Plug numbers into the

equation.3. Solve for a variable.4. Check your answer.5. Determine which variable to

eliminate.6. Put the equations in standard

form.

Find two numbers whose sum is 18 and whose difference 22.

1. 14 and 42. 20 and -23. 24 and -64. 30 and 8

Solving Systems of Equations

So far, we have solved systems using graphing, substitution, and elimination. These notes go one step further and show how to use ELIMINATION with multiplication.

What happens when the coefficients are not the same?

We multiply the equations to make them the same! You’ll see…

Solving a system of equations by elimination using multiplication.

Step 1: Put the equations in Standard Form.

Step 2: Determine which variable to eliminate.

Step 3: Multiply the equations and solve.

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

Step 5: Check your solution.

Standard Form: Ax + By = C

Look for variables that have thesame coefficient.

Solve for the variable.

Substitute the value of the variableinto the equation.

Substitute your ordered pair intoBOTH equations.

1) Solve the system using elimination.

2x + 2y = 63x – y = 5

2) Solve the system using elimination.

x + 4y = 74x – 3y = 9

What is the first step when solving with elimination?

1. Add or subtract the equations.2. Multiply the equations.3. Plug numbers into the equation.4. Solve for a variable.5. Check your answer.6. Determine which variable to

eliminate.7. Put the equations in standard form.

Which variable is easier to eliminate?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

3x + y = 44x + 4y = 6

1. x2. y3. 64. 4

3) Solve the system using elimination.

3x + 4y = -14x – 3y = 7

What is the best number to multiply the top equation by to eliminate the x’s?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

3x + y = 46x + 4y = 6

1. -42. -23. 24. 4

Solve using elimination.

2x – 3y = 1x + 2y = -3

1. (2, 1)2. (1, -2)3. (5, 3)4. (-1, -1)

Find two numbers whose sum is 18 and whose difference 22.

1. 14 and 42. 20 and -23. 24 and -64. 30 and 8