A set of equations is given below: Equation A: e = 4f + 1 Equation B: e = 3f + 5 Which of the following is a step that can be used to find the solution to the set of equations?

Question

A set of equations is given below:

Equation A: e = 4f + 1

Equation B: e = 3f + 5

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

 4f + 1= 3f 4f = 3f + 5 4f + 5 = 3f + 1 4f + 1 = 3f + 5

Answer 1

If I understand you answer correctly you have two linear equations:

Equation A: e=4f+1

Equation B: e=3f+5

This is a system of linear equations. You can solve a system of linear equations if you have the same number of unknowns as equations.

Since e=4f+1 and e=3f+5 we set the two equations equal.

So 4f+1 = e =3f +5

4f+1 = 3f +5

4f- 3f +1 =3f -3f +5

f +1 = 5

f +1-1 = 5 -1

f = 4

Now that we have found f you can plug the value of f into any of the equations above to get the value of e.

e=4f +1 => e=4*4 +1 = 17. If we used the second equation e=3f +5 => 3*4+5 =17

As you can see e =17 when you plug the value of f in each equation. If you solve it correct this should always be the case so you can check you work that way!

My final answer is : e =17 and f = 4

Answer 2

Two expressions that are equal to the same value are equal to each other.

Since you have two expressions that are equal to e, they are equal to each other.

4f + 1 = 3f + 5

Now, you may proceed to solve that equation for the value of f.