Question

pls help asap
Consider the following pair of equations:


y = 3x + 3

y = x − 1


Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.

Answer 1

Answer:

(-2, -3)

Step-by-step explanation:

We are given y = 3x + 3 and y = x - 1.

We can substitute y = x + 1 into the y value for y = 3x + 3, so

x - 1 = 3x + 3  Now, we just subtract x from both sides.

-1 = 2x + 3  We subtract 3 from both sides.

-4 = 2x

2x = -4  We divide both sides by 2

x = -2  Now we have our x value - (-2, y)

Let's substitute the x value into both of the equations given.

1st equation:

y = 3(-2) + 3

y = -6 + 3

y = -3

2nd equation:

y = (-2) - 1

y = -3

We now know that both equations give us the same y value when x = -2 is substituted, therefore our solution is:

(-2, -3)

Answer 2

The solution for the pair of equations is (-2,-3).

What is a system of equation?

A system of equations is a set or collection of equations that you deal with all together at once. For a system to have a unique solution, the number of equations must equal the number of unknowns.

For the given situation,

The pair of equations are

y = 3x + 3 ------- (1)

y = x − 1 -------- (2)

Substitute the equation 2 in equation 1, we get

⇒ $x-1=3x+3$

⇒ $3x-x=-1-3$

⇒ $2x=-4$

⇒ $x=-2$

Now substitute x in equation 2,

⇒ $y=-2-1$

⇒ $y=-3$

Hence we can conclude that the solution for the pair of equations is (-2,-3).

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