Question

2e - 3f = 4

Answer 1

2e - 3f = 4

2e - 5f = 8

To solve this system of equations by addition, our first goal is to cancel

out one of the variables by adding the two equations together.

However, before we add, we need to cancel out a variable.

I would choose to cancel out the e's.

To do this, we need a 2e and a -2e and

here we have a 2e in both equations.

If we multiply the second equation by -1 however,

that will give us the -2e we are looking for.

So we have (-1)(2e - 3f) = (4)(-1).

So rewriting both equations, our first equation stays the same

but our second equation becomes -2e + 3f = -4.

Notice that every term in the second

equation has been multiplied by -1.

2e - 3f = 4

-2e + 5f = -8

Now when we add the equations together,

the e's cancel and we have 2f = -4 so f = -2.

To find e, plug -2 back in for f in the

first equation to get 2e - 3(-2) = 4.

Solving from here, e = -1.

Note that e comes before f in our final answer, (-1, -2).

To determine which variable should go first

in your answer, use alphabetical order.

Answer 2

Answer:

The value of e is -1 and f is -2.

Step-by-step explanation:

The steps are :

$2e - 3f = 4 - - - (1)$

$2e - 5f = 8 - - - (2)$

$2e - 3f - 2e - ( - 5f) = 4 - 8$

$2f = - 4$

$f = - 4 \div 2$

$f = - 2$

$substitute \: f = - 2 \: into \: (1)$

$2e - 3( - 2) = 4$

$2e + 6 = 4$

$2e = 4 - 6$

$2e = - 2$

$e = - 2 \div 2$

$e = - 1$