Question

Choose the graph that solves this system of equations.

y = 2x – 6
y = –4x + 3
Two lines that intersect at the origin. One line has a positive slope and the other has a negative slope. Two lines that intersect at about 2 comma negative one half. One line has a positive slope and the other has a negative slope. There is also a single dot at the origin. Two lines that intersect at about three halves comma negative 3. One line has a positive slope and the other has a negative slope. Two lines that both have a positive slope. They do not intersect on the part of the graph shown, but there is a single dot at the origin.

Answer 1

d

Explanation:

Two lines that intersect at the origin. One line has a positive slope and the other has a negative slope

Answer 2

Answer: Two lines that intersect at about three halves comma negative 3. One line has a positive slope and the other has a negative slope.

Explanation:

Given equations of line:

y = 2x – 6 ...(i)

y = –4x + 3 ...(ii)

On comparing with y=mx+c (slope-intercept form), where m= slope ,= y-intercept.

(i) has positive slope (2) and (ii) has negative slope(-4).

Eliminate (ii) from (i), we get

0 = 6x-9

⇒ 6x=9

⇒
`x=\frac32`

Put value of x in (i), we get

`y=2(\frac32)-6\\\\\Rightarrow\ y=3-6=-3`

Point of intersection = (three halves, negative 3)