anyway

1.

add them equations, the y’s will cancel

x+2y=4

3x-2y=4 +

4x+0y=8

4x=8

divide by 4 both sides

x=2

sub back

x+2y=4

2+2y=4

minus 2

2y=2

divide 2

y=1

x=2

y=1

(x,y)

(2,1) is solution

2.

the solution is where they intersect

multiply 2nd equation by 2 and add to first

4x-14y=6

-4x+14y=-6 +

0x+0y=0

0=0

infinite solutions

that is because they are actually the same line

the solutions are (x,y) such that they satisfy -2x+7y=-3 or 4x-14y=6 (same equaiton)

infinite solutions

3.

multiply first equation by 2 and add to first

4x+2y=-6

1x-2y=-4 +

5x+0y=-10

5x=-10

divide by 5 both sides

x=-2

sub bac

x-2y=-4

-2-2y=-4

add 2

-2y=-2

divide by -2

y=1

x=-2

y=1

(x,y)

(-2,1)

4.

coincident means they are the same line

so

we see that we have to multiply 4 by 2 to get 8

multiply top equation by 2

8x+10y=16

8x+By=C

B=10 and C=16

5.

a. false, either 0, 1, or infinity solutions

change the word ‘two’ to ‘one’ or ‘zero’ or ‘infinite’, or change ‘can’ into ‘can’t’

b.false

‘sometimes’ to ‘always’

c. true

d. false, change ‘sometimes’ to ‘always’

EC

total cost=150

TC=childC+adultC

TC=3c+5a

150=3c+5a

40 tickets, c+a

40=c+a

the equations are

150=3c+5a and

40=c+a

eliminate

multiply 2nd equaton by -3 and ad to first one

150=3c+5a

-120=-3c-3a +

30=0c+2a

30=2a

divide by 2

15=a

sub back

40=c+a

40=c+15

minus 15

25=c

25 children tickets and 15 adult tickets were sold

ANSWERS:

1.

(2,1) is solution

2.

infinite solutions

3.

(-2,1)

4.

B=10 and C=16

5.

a. false,

change the word ‘two’ to ‘one’ or ‘zero’ or ‘infinite’, or change ‘can’ into ‘can’t’

b.false

‘sometimes’ to ‘always’

c. true

d. false, change ‘sometimes’ to ‘always’

EC

the equations are

150=3c+5a and

40=c+a

25 children tickets and 15 adult tickets were sold