Question

Which of the following equations has the same solutions as the equation 3x+2y=-12? Check all that apply.

A) 3x-2y= 12
B) -3x-2y= 12
C) 15x+10y= -60
D) 6x+2y= -12
E) 6x+4y= -24
F) 1.5x+y= -6
G) x+ 2/3 y= -12

Answer 1

Answer:

B, C, E, F

Step-by-step explanation:

Multiplying the equation by a constant does not change the solution set. When some terms are changed and others are not, the equation is a different equation.

A) different equation

B) multiplied by -1

C) multiplied by 5

D) different equation

E) multiplied by 2

F) multiplied by 1/2

G) different equation

Answer 2

ANSWER

$B,C,E \: and \: F$



EXPLANATION

The given equation is
$3x + 2y = - 12$

The solution to this equation can be found by making y the subject.

$\Rightarrow \: 2y = - 3x - 12$


$\Rightarrow \: y = - \frac{3}{2} x - 6$
This equation has infinitely many solution. Any real value we choose for x, there is a corresponding y-value.



To find which of the given options also has the same solution, we make y the subject.


A

$3x - 2y = 12$


$\Rightarrow \: - 2y = - 3x + 12$


$\Rightarrow \: y = \frac{3}{2} x - 6$


This is not the same as the given equation.


B


$- 3x - 2y = 12$


$\Rightarrow \: - 2y = 3x + 12$


$\Rightarrow \: y = - \frac{3}{2} x - 6$

This solution is the same as the one given.




C.
$15x + 10y = - 60$


$\Rightarrow \: 10y = - 15x - 60$



$\Rightarrow \: y = - \frac{15}{10} x - \frac{60}{10}$


$\Rightarrow \: y = - \frac{3}{2} x - 6$


This is the same as the above solution.


D.
$6x + 2y = - 12$



$\Rightarrow \: 2y = - 6x - 12$


$\Rightarrow \: y = - 3 x - 6$

This is not the same as the one given.


E.

$6x + 4y = - 24$


$\Rightarrow \: 4y = - 6x - 24$


$\Rightarrow \: y = - \frac{6}{4} x - \frac{24}{4}$

$\Rightarrow \: y = - \frac{3}{2} x - 6$

This is the same as the one given.


F.

$1.5x + y = - 6$


$\Rightarrow \: y = - 1.5x - 6$


$\Rightarrow \: y = - \frac{3}{2} x - 6$

Thus is the same as the one given.



G.
$x + \frac{2}{3} y = - 12$


$\Rightarrow \: \frac{2}{3} y = - x - 12$


$\Rightarrow \: y = - \frac{3}{2} x - 12 \times \frac{3}{2}$

$\Rightarrow \: y = - \frac{3}{2} x - 18$


This is not the same as the one given.