Question

1.

A set of equations is given below:

Equation S: y = x + 9
Equation T: y = 2x + 1

Which of the following steps can be used to find the solution to the set of equations? (4 points)



x = 2x + 1
x + 9 = 2x
x + 1 = 2x + 9
x + 9 = 2x + 1
2.
A system of equations is given below:

y = –2x + 1
6x + 2y = 22

Which of the following steps could be used to solve by substitution? (4 points)



6x + 2(–2x + 1) = 22
–2x + 1 = 6x + 2y
6(–2x + 1) + 2y = 22
6(y = –2x + 1)
3.
Solve the system of equations and choose the correct answer from the list of options.

d + e = 12
–d + e = –8

Label the ordered pair as (d, e). (4 points)



(0, 0)
(2, 10)
(10, 2)
(12, 0)

Answer 1

x + 9 = 2x + 1

Explanation:

Answer 2

1. x+9=2x+1. This is because both of the equations equal and define the value of y, and therefore must be equivalent.

2. The answer is the first one listed. When you substitute for y, the equation -2x+1, which defined y should be put in place of the variable y in the second equation.

3. Add the equations to eliminate
2e=4
e=2

Then plug the e value in
d+2=12
d=10

Final answer: (10,2)