Question

Question 10(Multiple Choice Worth 1 points)

(8.01 MC)

Two lines, A and B, are represented by the equations given below:

Line A: y = x − 6
Line B: y = 3x + 4

Which of the following shows the solution to the system of equations and explains why?

(−5, −11), because the point satisfies both equations
(−5, −11), because the point does not lie on any axis
(−3, −5), because the point satisfies one of the equations
(−3, −5), because the point lies between the two axes

Answer 1

y = x − 6

y = 3x + 4

y is isolated in both equations, thus, you can set x - 6 and 3x + 4 equal to each other to solve for x.

x - 6 = 3x + 4

-2x - 6 = 4

-2x = 10

x = -5

Substitute -5 for x into either of the original equations to find y.

y = x - 6

y = -5 - 6

y = -11

Plug both x- and y-values into each original equation to check whether these values satisfy both equations.

y = x - 6 --> -11 = -5 - 6 --> -11 = -11 --> True

y = 3x + 4 --> -11 = 3(-5) + 4 --> -11 = -15 + 4 --> -11 = -11 --> True

Answer:

(−5, −11), because the point satisfies both equations.

Answer 2

we are given

Line A: y = x − 6

Line B: y = 3x + 4

so, we can solve it

we can set them equal

and then we can solve for x

`y=x-6=3x+4`

now, we can solve for x

`-2x=10`

`x=-5`

now, we can find y

`y=-5-6`

`y=-11`

so, we will get intersection points as

(x,y)=(-5,-11)

so, option-A........Answer