Question

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

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,

$y - \frac{(7 - y)}{2} = 1$

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,

$x = - \frac{9}{2}$

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

$y = 3( - \frac{9}{2}) - 7$

This implies that,

$y = - \frac{27}{2} - 7$

This gives us,

$y = \frac{ - 27 - 14}{2}$

$y = \frac{ - 41}{2}$

The solution set is

{$( - \frac{9}{2} , - \frac{41}{2} )$}

The correct answer is B.