Question

Algebra - Two Questions

1. A system of linear equations is shown​ below as well as the first steps that Raffi is using to solve this system of linear equations by substitution. Choose the statement that best describes how Raffi is progressing toward a solution.

7x+y=4

3x−2y=3

Solution: Solve the first equation to obtain y=−7x+4. Substitute this into the second equation to get 3x−2⋅−7x+4=3.


2. Solve the following system by the substitution method.

2x−y=−4

−5x+3y=14

Answer 1

1. Raffi forgot to place the substituted expression in parentheses.

2. (2, 8)

Explanation:

If you are taking the Solving Systems With Substitution Quick Check from Connexus here are all of the answers:

1. Solve one linear function in terms of one of its variables.

2. Substitute 3y from the second equation for x in the first equation.

3. Raffi forgot to place the substituted expression in parentheses.

4. Yes, because substituting the given ordered pair yields two true expressions.

5. (2, 8)

Answer 2

The answer is below

Explanation:

1) Below are the linear equations.

7x+y=4 (1)

3x−2y=3 (2)

The above linear equations are a system of equations. The substitution method is a technique for solving systems of linear equations.

Given that:

7x + y = 4

y = 4 - 7x

substitute y = 4 - 7x in equation 2, hence:

3x - 2(4 - 7x) = 3

3x - 8 + 14x = 3

17x = 3 + 8

17x = 11

x = 11/17

Put x = 11/17 in y = 4 - 7x

y = 4 - 7(11/17)

y = -9/17

2) 2x−y=−4 (1)

−5x+3y=14 (2)

From equation 1:

2x−y=−4

y = 2x + 4

Put y = 2x + 4 in equation 2:

-5x + 3(2x + 4) = 14

-5x + 6x + 12 = 14

x + 12 = 14

x = 2

Put x = 2 in y = 2x + 4:

y = 2(2) + 4

y = 8