Question

How many solutions does this linear system have?

Answer 1

Answer:

B. one solution: (–0.6, 1.6)

Step-by-step explanation:

Answer 2

Equation 1: $y = \frac{2}{3}x+2$
Equation 2: $6x-4y=-10$

Substitute Equation 1 into Equation 2

$6x-4[ \frac{2}{3}x+2]=-10$
$6x- \frac{8}{3}x -8=-10$
$\frac{10}{3}x-8=-10$
$\frac{10}{3}x=-10+8$
$\frac{10}{3}x=-2$
$10x=-6$
$x=- \frac{6}{10}$
$x=-0.6$

Substitute x = -0.6 into either Equation 1 or Equation 2 to work out 'y'

$y= \frac{2}{3}(-0.6)+2 = 1.6$

The linear system only have one solution (-0.6, 1.6)

Correct answer: B