Question

Which value of x satisfies both -9x + 4y = 8 and -3x − y = 4 given the same value of y?

Answer 1

Answer:

C

Step-by-step explanation:

Since y will have same value, y doesn't really matter. Thus,

We can solve for y in the 2nd equation as:

-3x - y = 4

-3x - 4 = y

Now we can plug it into the first and solve for x:

-9x + 4y = 8

-9x + 4(-3x - 4) = 8

-9x - 12x - 16 = 8

-21x = 8 + 16

-21x = 24

x = 24/-21

x = -8/7

Correct answer is C.

Answer 2

Answer: Option C

C-8/7

Step-by-step explanation:

We have the following equations

 $-9x + 4y = 8$ and $-3x - y = 4$

We want to find a value of x that satisfies both equations and obtains the same value of y.

To find the value of x, clear the value of y in both equations

$-9x + 4y = 8\\\\-9x + 4y -8 = 0\\\\-9x -8 = -4y\\\\y = \frac{9}{4}x +2$

------------------------------

$-3x - y = 4\\\\\-3x -y - 4 = 0\\\\y = -3x -4$

Now solve both equations and solve for x.

$\frac{9}{4}x +2 = -3x -4\\\\\frac{21}{4}x = -4-2\\\\\frac{21}{4}x = -6\\\\21x = -24\\\\x = -\frac{24}{21}\\\\x = -\frac{8}{7}$

The answer is $x = -\frac{8}{7}$