Question

HEEEEEELLLLLLLPPPPPP MMMMMMMMMMEEEEEEEEE Two lines, A and B, are represented by equations given below: Line A: y = x − 2 Line B: y = 3x + 4 Which of the following shows the solution to the system of equations and explains why? (−3, −5), because the point does not lie on any axis (−3, −5), because the point satisfies both equations (−4, −8), because the point satisfies one of the equations (−4, −8), because the point lies between the two axes

Answer 1

It sounds like you've already let this problem get ahold of you and start
squeezing the air out of you. So first, I want you to take a deep, cleansing
breath, let it out slowly, and then try to think:

Before you get all involved and flustered, what is the solution to a system
of equations ? What does "solution" even mean ? You can't find a solution
unless you know what one looks like, so you recognize it when you see it.

The "solution" to one equation is the number that makes the equation true
when you write the number in place of the variable. There can be more than
one solution, and there may be no solution at all. It depends on the equation.

The "solution" to a system of equations is a set of numbers, that makes all of
the equations true when you write the numbers in place of all the variables in
them.

A good way to think about the solution to a system of equations is to imagine
that you draw the graph of each equation, and look for a place where the lines
cross. That point is a solution of the system of equations, because it's a point
that's on the graph of both equations. The (x, y) numbers for that point make
both equations true when you write them in place of 'x' and 'y' in each equation.

Now look at the choices you have for an answer to this question. You haven't
numbered or lettered the choices, so it's hard to tell you which one it is. But
you should have no trouble finding the right choice, because there's only one
of them up there that says anything about satisfying both equations.

Answer 2

(-3,-5) because the point satisfies both equations.

Explanation:

We are given that two lines A and B

Line A:
`y=x-2`

Line B:
`y=3x+4`

We have to find the solution of the given system of equation and explain .

Using elimination method

Eliminate y by subtracting equation first from equation second then, we get

`2x+6=0`

`2x=-6`

`x=(-6)/(2)=-3`

Substitute x=-3 in equation first

`y=-3-2=-5`

Hence, the solution of given system of equation is (-3,-5).

Substitute x=-3 and y=-5 in first equation then , we get

`-5=-3-2=-5`

LHS=RHS

Hence, (-3,-5) satisfies the the equation.

Substitute x=-3 and y=-5 in second equation

Then, we get

`-5=3(-3)+4=-5`

LHS=RHS

Hence, (-3,-5) satisfies the equation.

Hence, (-3,-5) is the solution of the system of equations because the point satisfies both equations.

Answer:(-3,-5) because the point satisfies both equations.