Question

Question 24 Multiple Choice Worth 1 points)

(8.01 MC)
Two lines, A and B, are represented by equations given below:
Line A: y = x - 4
Line B: y = 3x + 4
Which of the following shows the solution to the system of equations and explains why?
0 (-3,-5), because the point satisfies one of the equations
0 (-3,-5), because the point lies between the two axes
(-4,-8), because the point satisfies both equations
(-4, -8), because the point does not lie on any axis

Answer 1

Given:

The system of equations is:

Line A:
`y=x-4`

Line B:
`y=3x+4`

To find:

The solution of given system of equations.

Solution:

We have,

`y=x-4` ...(i)

`y=3x+4` ...(ii)

Equating (i) and (ii), we get

`x-4=3x+4`

`-4-4=3x-x`

`-8=2x`

Divide both sides by 2.

`-4=x`

Substituting
`x=-4` in (i), we get

`y=-4-4`

`y=-8`

The solution of system of equations is (-4,-8).

Now verify the solution by substituting
`x=-4, y=-8` in the given equations.

`-8=-4-4`

`-8=-8`

This statement is true.

Similarly,

`-8=3(-4)+4`

`-8=-12+4`

`-8=-8`

This statement is also true.

Therefore, (-4,-8) is a solution of the given system of equations, because the point satisfies both equations. Hence, the correct option is C.