ALGEBRA II HONORSALGEBRA II HONORS

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SOLUTIONS OF SYSTEMS OF SOLUTIONS OF SYSTEMS OF LINEAR EQUATIONSLINEAR EQUATIONS

1) Solve by graphing.

2x + y = 8

3x – 2y = -2

Solve for y.

y = -2x + 8

Find the intercepts.

x-int : -2/3

y-int : 1

The point of intersection

is (2, 4)

Note that 2(2) + 4 = 8 and

3(2) – 2(4) = -2

2) Solve by substitution.

2x + y = 8

3x – 2y = -2

Look for the equation where solving for x or for y is easiest.

Solve for y in the top equation.

y = -2x + 8

Next, substitute into the other equation and solve.

3x – 2y = -2

3x – 2(-2x + 8) = -2

3x + 4x – 16 = -2

7x – 16 = -2

7x = 14

x = 2Substitute 2 for x for find y.

y = -2(2) + 8

= 4

Therefore, the answer is (2, 4)

3) Solve using elimination

(linear combination)

2x + y = 8

3x – 2y = -2

The goal is to make opposites for one of the variables and add the equations together.

Multiply the top equation by 2 to make 2y on top to go along with the -2y on bottom.

2 • (2x + y) = 8 • 2

3x – 2y = -2 4x + 2y = 16

3x – 2y = -2

7x = 14

x = 2

Substitute 2 for x into either original equation to find y.

2(2) + y = 8

4 + y = 8

y = 4

Therefore, the answer is (2, 4)

METHODS FOR SOLVING SYSTEMS OF EQUATIONS :

1)Graphing

2)Substitution

3)Elimination (linear combination)

4)????

5)????

Solve using the method of your choice.

4) 3x – 7y = 31

2x + 5y = 11

5) 4x + 3y = 10

5x - y = 22

6) 2x – 3y = 12

y = -2x + 4

Just in case you want it!!

7) y = x + 1 y = x – 2

8) 2x – 4y = -16

-x + 2y = 8

If the variables cancel

true statement

infinite solutions

same lines

false statement

no solutions

Parallel lines

8) 4x – 3y = 11

5x – 6y = 9

9) 3 5 + = -10x y9 10 + = -15x y

NAMES FOR SYSTEMS OF EQUATIONSNAMES FOR SYSTEMS OF EQUATIONS

Inconsistent equations

Parallel lines

Dependent equations

Coincidental lines

Independent equations

Intersecting lines