Question

PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
(08.03)Solve the system of equations and choose the correct answer from the list of options.

x − y = 7
y = 3x + 12

2 over 19 comma 2 over 33
negative 2 over 19 comma negative 33 over 2
negative 19 over 2 comma negative 33 over 2
19 over 2 comma 33 over 2

Answer 1

Do you understand what the question is asking for?
When you solve 2 equations at the same time, you're solving for 2 different variables (letters) at the same time; this means you're trying to find the value of x and the value of y that makes each equation true.

For example, the equation
2x = 4
can be solved with the solution that x = 2. This is only one equation, however.

When we solve for 2 equations simultaneously (at the same time) we need to consider just one equation first. There are a few ways of solving simultaneous equations - the easiest way in your situation is to use SUBSTITUTION.

Let's work through an example.
x + y = 5 ... (equation 1)
x - y = 1 ... (equation 2)

First of all, we choose an equation (it doesn't matter which!). Let's choose equation (2).
Let's choose a variable (again, it doesn't matter which one we choose!) that we want all by itself... I'm going to choose x.
If we rearrange the equation, we get
x = 1 + y (we just added y to both sides of the equation)
We then SUBSTITUTE this "new" equation into (1), so we get
(1+y) + y = 5, which we can then solve
1 + 2y = 5
2y = 4
y = 2

Now that we have y = 2, we can SUBSTITUTE that back into either equation to find x. Let's choose (2) again (it doesn't matter which one we choose here either!)
x - y = 1, so
x - 2 = 1
x = 3

So we end up with x = 3, y = 2. Try a similar approach in your question.