Question

A set of equations is given below:

Equation A: a = 5b + 1
Equation B: a = 3b + 5

Which of the following is a step that can be used to find the solution to the set of equations? (5 points)


5b + 1= 3b
5b = 3b + 5
5b + 1 = 3b + 5
5b + 5 = 3b + 1

Answer 1

The correct answer is 5b + 1 = 3b + 5. In order to find the answer to a system of equations, the two equations must be set equal to each other. For instance, if we had the equations x = y + 1 and x = 3y - 1, we would set the two equations equal to one another to find the answer.

x = y + 1
x = 3y - 1
y + 1 = 3y - 1
1 = 2y - 1
2 = 2y
1 = y

x = y + 1
x = 1 + 1
x = 2

You can use the same procedure with this system of equations.

5b + 1 = 3b + 5
2b + 1 = 5
2b = 4
b = 2

a = 5b + 1
a = 5(2) + 1
a = 10 + 1
a = 11

Hope this helps!

Answer 2

C.
`5b+1=3b+5`

Explanation:

We have been given a set of equations as:

Equation A:
`a=5b+1`

Equation B:
`a=3b+5`

We can see that the given set of equations represent system of linear equation.

We will use substitution property of equality, which states when
`x=y`, then x can be substituted in any equation in place of y and y can be substituted in place of x in any equation as well.

To solve our given system of equations we need to equate our given equations as:

`5b+1=3b+5`

Therefore, option C is the correct choice.