50 points!

1. use the graph to state the solution for the system. (in other words, what is the solution for the system? )

x + 2y = 4 (line a)

3x – 2y = 4 (line b)

2. how many solutions are there to the following system of equations? use any method you like, but be sure to show all work.

4x – 14y = 6

–2x + 7y = –3

3. what is the solution to the system of equations? use any method you like, but be sure to show all work.

2x + y = -3

x – 2y = -4

4. the system of equations is coincident. what are the values for b and c that make the system coincident?

4x + 5y = 8

8x + by = c

5. identify whether the statement is true or false. if the statement is false, change one word to transform it into a true statement.

a. two linear equations can have two solutions.

b. lines with no solutions are sometimes parallel.

c. the solution of a system of linear equations is the coordinate point where their graph intersects.

d. equations that have different slopes sometimes have one solution.

ec: write and solve system of equations that can be used to solve the following problem.

each child ticket for a ride costs $3, while each adult ticket costs $5. if the ride collected a total of $150, and 40 tickets were sold, how many of each type of ticket were sold? where c is the number of child tickets and a is the number of adult tickets.

Well, 50 points total given, 25 points per user  and 13 bonus for brainliest

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