Question

What is the solution of this linear system? Multiple Choice

Answer 1

These are pretty easy once you know how to do them. So let me explain them to you! 

We have two equations:
4x + y = -1
y = -2x + 3

Below is an EXAMPLE PROBLEM with a thorough explanation: And below that is THE PROBLEM
When they are given to us like this with the same variables it means that the values are the same. 

It would be the same as saying this: 
x + 2 = 4
x = 4 - 2

x in both equations is the same number. And in cases where they want us to find two VARIABLES with two equations. It's quite simple. You take one of the equations and solve it for ONE of the variables. Example: 

x + y = 2

I'll solve for x in this case. 

x + y - y = 2 - y
x = 2 -y

You then take the value you got when you solve for x, and substitute it in for x in the 2nd equation which would be given to you. 
Let's say the 2nd equation in this example is... 

2x + 3y = 4

Substitution is the same thing you do whenever a problem says something like "what is the value of the function when x = 3." You plug in that entire value (3) wherever you see x. In this case you plug in x = 2 - y, anywhere you see x. 

2(2 - y) + 3y = 4

Solve for y. 

4 - 2y + 3y = 4
4 + y = 4
y = 0 

You then plug in that value into the previous function. 
x + y = 0
Where y = 0

x + 0 = 2
x = 2 

Check it by putting it in the other equation. 
2*2 + 3*0 = 4 
4 + 0 = 4
4 = 4 

See how that works? Now let's do the same thing, but with our problem!

4x + y = -1
y = -2x + 3

In this case they gave us two equations where one is already solved for a variable. (Keep in mind "solved" means that only that variable is on that side of the equal sign)

So we will sub in y = -2x + 3 wherever we see y in the OTHER equation!

4x + y = -1
4x + (-2x + 3) = -1
4x - 2x + 3 = -1

Combine like terms!
2x + 3 = -1
2x + 3 - 3 = -1 - 3
2x = -4
2x/2 = -4/2

x = -2

Plug that number into the other equation (technically you can plug into either one, but it is a good habit to switch so that you won't forget to switch in the first step when you solve for one of the two variables).

y = -2x + 3
y = -2(-2) + 3
y = 4 + 3
y = 7

Plug both numbers in the OTHER equation.

4x + y = -1
4(-2) + 7 = -1
-8 + 7 = -1
-1 = -1

So your answer is...!
x = -2 and y = 7. The answers are in the form of points. Which look like this: (x,y)

So plug in the values for x and y to get your answer which should come out to be: 

a. (-2,7)