Question

Question 1(Multiple Choice Worth 5 points)

(8.01 LC)

Two lines, A and B, are represented by the equations given below:

Line A: x + y = 2
Line B: 2x + y = 4

Which statement is true about the solution to the set of equations?
There are infinitely many solutions.
There are two solutions.
There is one solution.
There is no solution.
Question 7(Multiple Choice Worth 5 points)
(8.02 MC)

Which of the following graphs shows a pair of lines that represent the equations with a solution (−5, 2)?
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 2 units to the right and 5 units down.
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 5 units to the right and 2 units down.
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 5 units to the left and 2 units up.
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 2 units to the left and 5 units up.

Answer 1

The third answer is correct

Answer 2

Question 1:

Substitution.

x+y=2

y=-x+2

Put this in the next equation as y:

2x+(-x+2)=4

2x-x=x

x+2=4

x=2

Put this into the first equation.

(2)+y=2

Subtract 2 from both sides.

y=0

Solution: (2,0)

There is only one solution.

Question 7:

A solution to a set of equations is where the two lines agree on an ordered pair.

The 2 lines should intersect at the solution (--5,2)

Long story short, it's the third option.