Question

Which pair of words describes this system of equations 3y=9x-6 2y+6x=4

Answer 1

Answer:

Consistent and dependent

Step-by-step explanation:

Given

$3y = 9x - 6$

$2y + 6x = 4$

Required

The words that describe the equations

Make y the subject in (2)

$2y + 6x = 4$

Collect like terms

$2y = 4 - 6x$

Divide through by 2

$y = 2 - 3x$

Substitute: $y = 2 - 3x$ in (1)

$3y = 9x - 6$

$3(2 - 3x) = 9x - 6$

$6 - 9x = 9x - 6$

Collect like terms

$9x+9x = 6+6$

$18x = 12$

Solve for x

$x = \frac{12}{18}$

Simplify

$x = \frac{2}{3}$

Substitute $x = \frac{2}{3}$ in $y = 2 - 3x$

$y = 2 - 3*\frac{2}{3}$

$y = 2 - 2$

$y =0$

So, we have:

$x = \frac{2}{3}$ and $y =0$

The system is consistent because it has at least 1 solution

The system is dependent because it has more than 1 solution