Question

Question 1(Multiple Choice Worth 4 points)

(08.03)Consider the following set of equations:

Equation C: y = 2x + 8
Equation D: y = 2x + 2

Which of the following best describes the solution to the given set of equations?

No solution
One solution
Two solutions
Infinite solutions
Question 2(Multiple Choice Worth 4 points)
(08.01)Consider the following equations:

−x − y = 1
y = x + 3

If the two equations are graphed, at what point do the lines representing the two equations intersect?

(−1, 2)
(−2, 1)
(1, −2)
(2, −1)
Question 3(Multiple Choice Worth 4 points)
(08.01)Two lines, A and B, are represented by the following equations:

Line A: 2x + 2y = 8
Line B: x + y = 3

Which statement is true about the solution to the set of equations?

It is (1, 2).
There are infinitely many solutions.
It is (2, 2).
There is no solution.
Question 4(Multiple Choice Worth 4 points)
(08.03)Consider the following set of equations:

Equation A: y = −x + 5
Equation B: y = 6x − 2

Which of the following is a step that can be used to find the solution to the set of equations?

−x = 6x + 2
−x − 2 = 6x + 5
−x + 5 = 6x – 2
−x + 5 = 5x
Question 5(Multiple Choice Worth 4 points)
(08.01)Consider the following system of equations:

y = −x + 2
y = 3x + 1

Which description best describes the solution to the system of equations?

Line y = −x + 2 intersects line y = 3x + 1.
Lines y = −x + 2 and y = 3x + 1 intersect the x-axis.
Lines y = −x + 2 and y = 3x + 1 intersect the y-axis.
Line y = −x + 2 intersects the origin.
Question 6 (Essay Worth 5 points)
(08.01) The graph shows two lines, Q and S.
Pls answer all correct due in 5 minutes
A coordinate plane is shown with two lines graphed. Line Q has a slope of one half and crosses the y axis at 3. Line S has a slope of one half and crosses the y axis at negative 2.

How many solutions are there for the pair of equations for lines Q and S? Explain your answer.
(08.03) Consider the following pair of equations:

y = 3x + 3
y = x − 1

Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.

Answer 1

Explanation:

Q1) We know that y = 2x+8, and y = 2x+2, this means that the equations should be equivalent (they both = y)

2x + 8 = 2x + 2

This is impossible, so there are no solutions. (Try plugging in for x if you don't get it - answering fast as per your request!)

Q2)

We can rearrange the first equation. -x - y = 1

1. Add y to both sides

2. Subtract 1 from both side

So now we have : y = -x-1

y = x + 3

These intersect when again, they are equivalent so we solve the equation:

x + 3 = -x-1

2x + 3 = -1

2x = -4

x = -2

So the answer must be (1,-2) ... (plug x back in for y usually to get the points, but here it's MC and only one has x = -2)

Q3)

2x + 2y = 8 - Line A can be divided by 2 to look more like Line B

Line A = x+y = 4

Similar to problem 1. x+y cannot equal both 3 AND 4, there is no solution.

Q4)

Again, same concept as problem 1. Both A and B are equal to Y, so we can find the solution by setting the equal:

-x +5 = 6x -2

Q5)

Same thing!

-x +2 = 3x +1

4x + 1 = 2

4x = 1

x = 1/4

This means that the two lines must intersect at some point, the point at which two lines intersect is the solution to their systems.

Line y = −x + 2 intersects line y = 3x + 1.

Q6)

Q = 0.5x + 3

S = 0.5x - 2

Lines Q and S have the same slope but different y-intercepts. This means they are parallel and will never intersect, so they are no solutions for their system of equations.

Q7)

Substitution means we want to solve for a variable in one equation, and plug this into the second, so we obtain a solvable, 1 variable equation.

We know y = 3x +3, and our second equation is equal to y. So we can substitute this y for 3x +3.

EQ1: y = 3x +3

EQ2: y = x-1 (substituting y for 3x+3 into this equation)

3x +3 = x - 1

-x -x

-3 -3

2x = -2

x = -1

plugging this into the simpler equation:

y = (-1) -1

y = -2

So the solution is (-1,-2).

Hope I answered it in time and you can make up an excuse if it's a little late!