Solve each system of equations using substitution. Show all work.

1) y = 2x - 5

4x - y = 7

2) 2x - 3y = 12

x = 4y + 1

3) y = 5 - x

x - 4y = 10

1.

y=2x-5

sub that for y

4x - (2x-5) = 7

distribute

4x-2x+5=7

2x+5=7

2x=2

x=1

sub back

y=2x-5

y=2 (1) - 5

y=2-5

y=-3

(1,-3)

2. x=4y+1

sub that for x

2 (4y+1) - 3y=12

8y+2-3y=12

5y+2=12

5y=10

y=2

sub back

x=4y+1

x=4 (2) + 1

x=8+1

x=9

(9,2)

3. y=5-x

sub that for y

x-4 (5-x) = 10

x-20+4x=10

5x-20=10

5x=30

x=6

sub back

y=5-x

y=5-6

y=-1

(6,-1)

soluitons

1. (1.-3)

2. (9,2)

3. (6,-1)