Question

What is the value of the x variable in the solution to the following system of equations?
7x - 2y = 21
4x + y = 57

21

-21

9

-9

Answer 1

What methods of solving systems of linear equations have you been taught/ do you want to use on this one?

Answer 2

Ok, look at the second equation:
4x + y = 57
Whenever you have a variable already alone (ie it has no number beside it)
that usually makes life easier for you.

In this case, try to isolate y (in other words, put it on one side of the equation, and all the rest on the other side)

Go ahead :D

Answer 3

4x + y = 57

Now add (-4x) to both sides

4x + y - 4x = 57 - 4x
4x - 4x + y = 57 - 4x
y = 57 - 4x

Get me so far? :)

Answer 4

x - 2y = 21
4x + y = 57

We take the second equation, and multiply everything by 2

2(4x + y) = 2(57)
8x + 2y = 114

We replace the second equation with this one

7x - 2y = 21
8x + 2y = 114

Now we add up all those on the left side, and all those on the right

7x - 2y + 8x + 2y = 21 + 114
15x = 135 (the y got cancelled out!)
x = 9 (divided both sides by 15)

So now that we know that x = 9, then we substitute it for the x in the first equation
7x - 2y = 21
7(9) - 2y = 21
63 - 2y = 21
- 2y = 21 - 63
- 2y = -42
y = 21 (dividing both sides by -2)

So x=9 and y=21
To be safe, let's try it with the second equation as well

4x + y = 57
4(9) + 21 = 57
36 + 21 = 57
57 = 57 (it works! )

Thus, we're sure that
x = 9
and
y = 21

END

Hope that helps
And remember to study the process I went through to get to the answer