Systems of Equations - Grill

Substitution

100

y = -2

4x - 3y = 18

(3, -2)

200

y = 5x + 1

y = -4x 10

(1,6)

300

y = 6x - 11

-2x - 3y = -7

(2,1)

400

-4x + y = 6

-5x - y = 21

(-3, -6)

500

y = -10x - 0.5

-50x - 10y = 105

(2, -41/2) or (2, -20.5)

Substitution- Solve for one variable

100

−3x − 3y = 3

 y = −5x − 17

(−4, 3)

200

−5x + y = −2 

−3x + 6y = −12

(0, -2)

300

5x - y = 5

-x + 3y = 13

(2,5)

400

−7x − 2y = −13 

x − 2y = 11

(3,-4)

500

−3x − 4y = 2 

3x + 3y = −3

(-2,1)

Elimination

100

-x + y = 7

x + y = 1

(-3, 4)

200

-4x + 5y = 17

4x + 6y = -6

(-3 , 1 )

300

a + 4b = -4

a + 10b = -16

( 4 , -2 )

400

2x + y = -8

x - y = 2

( -2 , -4 )

500

16x − 10y = 10

−8x − 6y = 6

(0, -1)

Elimination Using Multiplication

100

x + y = 2

-3x + 4y = 15

( 1 , -3 )

200

2x + 5y = 11

4x + 3y = 1

( -2 , 3 )

300

12x - 3y  = -3

6x + y = 1

( 0 , 1 )

400

16x − 10y = 10 

−8x − 6y = 6

(0, -1)

500

3x − 2y = 2 

5x − 5y = 10

( -2 , -4 )

Which Method?

100

2x + y = 20

6x − 5y = 12

Substitution, solve for y in the first equation. Elimination, multiply the first equation by 5 or 3.

(7, 6)

200

−2x − y = −9 

5x − 2y = 18

Substitution, solve for y in the first equation. Elimination, multiply the first equation by 2.

(4, 1)

300

−5x − 8y = 17 

2x − 7y = −17

Elimination, multiply equations to find common multiple.

400

x + 3y = 1 

−3x − 3y = −15

Elimination (add)

(7, −2)

500

−5x + y = −2 

−3x + 6y = −12

Substitution, solve for y in the first equation. Elimination, multiply the first equation by 6.

(0, −2)