Algebra 2: Systems of Equations and Absolute Value Equations

Which Method is Best?

100

Which method would be best to solve the system below? (Graphing, Substitution, or Elimination)

x = 2

2x + 3y = 13

Substitution

x is already solved!

Plug in 2 directly in for x and solve for y!

200

Which method would be best to solve the system below? (Graphing, Substitution, or Elimination)

y = -3x + 2

6x + 2y = 1

Substitution

y is already solved for, just plug it in!

300

Which method would be best to solve the system below? (Graphing, Substitution, or Elimination)

3x + 2y = 4

-3x + y = 2

Elimination

Get rid of the x by adding!

400

Which method would be best to solve the system below? (Graphing, Substitution, or Elimination)

y = 1/2x + 2

y = 2x - 7

Graphing

Both equations are in y = mx + b form!

(Substitution could also work here)

500

Which method would be best to solve the system below? (Graphing, Substitution, or Elimination)

4x + y = 16

2x + 3y = -2

Elimination

Multiply the bottom equation by -2

(Or Substitution; Solve the first equation for y)

Solve by Substitution

100

Solve the system by Substitution method:

y = -2

4x - 3y = 18

(3, -2)

4x - 3(-2) = 18

4x = 12

x = 3

200

Solve the system by Substitution method:

2x - 3y = -1

y = x - 1

(4, 3)

2x - 3(x - 1) = -1

-x + 3 = -1

-x = -4 ---> x = 4

300

Solve the system by Substitution method:

y = x

y = -x + 6

(3, 3)

x = -x + 6

2x = 6

x = 3

400

Solve the system by Substitution method:

y = 5x - 1

2y = 3x + 12

(2, 9)

2(5x - 1) = 3x + 12

10x - 2 = 3x + 12

7x = 14

500

Solve the system by Substitution method:

-5x + y = -3

3x - 8y = 24

(0, -3)

y = -3 + 5x

3x - 8(-3 + 5x) = 24

3x + 24 - 40x = 24 ---> -37x = 0

Solve by Elimination

100

Solve the system using Elimination method:

x - y = 11

2x + y = 19

(10, -1)

Get rid of the y by adding!

3x = 30

x = 10

200

 Solve the system by using the Elimination method:

-6x + 5y = 1

6x + 4y = -10

(-1, -1)

Get rid of x by adding!

9y = -9

y = -1

300

Solve the system by using the Elimination method:

4x + 2y = 8

3x + 2y = 6

(2, 0)

Get rid of the y by subtracting!

x + 0 = 2

x = 2

400

Solve the system by using the Elimination method:

-3x + 3y = 3

-3x + 6y = -12

(-6, -5)

Get rid of the x by subtracting!

-3y = 15

y = -5

500

Solve the system by using the Elimination method:

5x + y = 9

10x - 7y = -18

(1, 4)

Multiply the top equation by -2

-10x - 2y = -18

10x - 7y = -18    ----> Then add!

Solve Absolute Value Equations 1

100

| z - 13 | =21

{-8, 34}

200

 | a - 6 | = 10

{16, -4}

300

3 * | 2a - 4 | = 0

{ 2 }

400

| 3b - 10 | = 2b

{ 10, 2 }

500

-3 * | 3t - 2 | - 12 = -6

{ No Solution }

Solve Absolute Value Equations 2

100

| x - 6 | = 35

{ 41, -29 }

200

 2 | x + 5 | = 22

{ 16, -6 }

300

3 | r - 4 | = -21

{ 3, -11 }

400

| p + 1 | + 10 = 5

{ No Solution }

500

2 * | 3x - 4 | + 8 = 6

{ 5/3 }