Question

1.) For the following system, use the second equation to make a substitution for x in the first equation.

3x + 2y = 7
x - y + 3 = 0
What is the resulting equation?
a. 3x - y - 3 + 2y = 7
b. 3(y - 3) + 2y = 7
c. 3y - 3 + 2y = 7

2.) Which of the following would not be the result of a substitution in the following system?

2x + y = 7
y - x = 1

a. 7 - 2x - x = 1
b. 2x + x + 1 = 7
c. 2(y + 1) + y = 7

3.)Solve the following system of equations by the substitution method.

8x = 2y + 5
3x = y + 7
What is the solution set?
a. {(-41/2, -9/2)}
b. {(-9/2, -41/2)}
c. ∅

Answer 1

1.)-b. 2)-.b.3)-b I am sure

Answer 2

QUESTION 1

The given system of equation is


`3x + 2y = 7 - - - (1)`
and


`x - y + 3 = 0 - - - (2)`

The question requires that, we make x the subject in equation (2) and put it inside equation (1).

So let us express x in terms of y in equation (2) and call it equation (3) to get,


`x = y - 3 - - - (3)`

We now substitute equation (3) in to (1) to obtain,


`3(y - 3) + 2y = 7`

Therefore the correct answer is B.

QUESTION 2

The given equations are

`2x + y = 7 - - - (1)`


`y - x = 1 - - - (2)`

First let us make all the four possible substitutions.

The first is to make y the subject in equation (2) and substitute in to equation (1) to get,


`2x + x+ 1 = 7`
The second one is to make x the subject in equation (2) and put in to equation (1) to get,


`2(y - 1) + y = 7`

The third one is to make y the subject in equation (1) and put it into equation (2) to get,


`7 - 2x - x = 1`

The fourth one is to make x the subject in equation (1) and put it in to equation (2) to get,


`y - ((7 - y))/(2) = 1`

By comparing to given options, C is not part of the four possible results.

Therefore the correct answer is option C.

QUESTION 3

The equations are

`8x = 2y + 5- - - (1)`


`3x = y + 7- - - (2)`

We make y the subject in equation (2) to get,


`y = 3x - 7 - - - (3)`

We substitute equation (3) in to equation (1) to get,


`8x = 2(3x - 7) + 5`

We expand to obtain,


`8x = 6x - 14+ 5`

We group like terms to get,


`8x - 6x = - 14+ 5`

This implies that,


`2x = - 9`

Therefore,


`x = - (9)/(2)`

We substitute this value into equation (3) to get,


`y = 3( - (9)/(2)) - 7`

This implies that,


`y = - (27)/(2) - 7`

This gives us,


`y = ( - 27 - 14)/(2)`


`y = ( - 41)/(2)`

The solution set is

{
`( - (9)/(2) , - (41)/(2) )`}

The correct answer is B.