Solving for a Variable

Rewrite the equations

100

2x + y = 4

m = -2x + 4

200

8x + 2y = 10

y = -4x + 5

300

-6x + 2y = 10

y = 3x + 5

400

6x + 3y = -12

y = -2x - 4

500

x + 8y = 24

y = -1/8x + 3

Two step

100

12 = 7a – 2

a = 2

200

-5 = 3c – 2

c = -1

300

–2 = m/3 + 4

m = – 18

400

–35 = –4x – 7

x = 7

500

4(z + 1) = 32

z = 7

Variables on both sides

100

13a – 14 = 10a – 2

a = 4

200

12a – 11 = 9a + 1

a = 4

300

26 + 5a – 10 = –4a + 1 + 4a

a = –3

400

6r + 2 – r = 2r + 4 + 3r

no solution (NS)

500

7m – 4m + 1 = 9m + 1 – 6m

Infinite Solutions

Are they equivalent?

100

Are they equivalent?:

2x=4 and 4x+5=13

Yes 

200

Are they equivalent?:

-2x+9=7 and -2x=2 

No

300

Are they equivalent?:

5x-4+3x=8 and 8x=12 

yes 

400

Are they equivalent?:

3/4x-7=2 and x=12 

yes

500

Are they equivalent?:

1.2x=2.4 and x-6=8 

no

Mix

100

6x+2=8

x=1

200

1.5(p+3)=18 

p=9

300

2.9y+2.7=1.1y-9.9

y=-7

400

5/4e+1/2=2e-1/2

e= 4/3

500

7.5x-4.1=6.7-4.5x

x= 0.9