Question

Solve the system of equations.
5x - y = 3 and -10x + 2y = -6
a (0, -3)
b (-3, 0)
c (3, 12)
d no solution
e infinitely many solutions

Answer 1

Which methods are you familiar with?

Answer 2

Uhm, none because i don't understand any of it and the lessons dont teach very well

Answer 3

Ok.
There are several methods for solving systems of equations.
Usually, all methods work on most problems.
The reason we may choose to use a method over another method for a specific system of equations, is that for a specific system, one method may be quicker than another method.

Answer 4

I'm going to explain to you the substitution method. This is one of the most basic methods that are learned.

Answer 5

Okay

Answer 6

In the substitution method, we do the following:
1. Solve one equation for one variable.
2. Substitute that variable in the other equation with what we got in step 1.
3. Solve for the variable that is left.
4. Once you know one variable, substitute its value into one of the original equations, and solve for the other variable.

Answer 7

Read the above.
Go over it a couple of times.
Even if you don't fully understand it at first, don't worry because we will follow the method to solve your system, and you will see the method at work.

Answer 8

using this method will result is a confusing answer in this case....

Answer 9

We don't know that until we start.
Let's start.

We see that the first equation has a term -y.
That makes that equation easier to solve for y than either equation to solve for x.

Let's start with the first equation and solve for y.

\(5x−y=3 \)

Answer 10

We subtract 5x from both sides:

\(−y=−5x+3\)

Now we have -y, but we want y, so we multiply both sides by -1:

\(y=5x−3\)

Answer 11

Thank you for helping, i have to go to my next class but i'll be on to look at what youve posted again later. Thanks again!

Answer 12

Now that we know what y is from the first equation, we substitute it into y of the second equation.

We write the second equation:

\(-10x + 2y = -6\)

We substitute 5x - 3 into y:

\(-10x + 2(5x - 3) = -6\)

We distribute the 2:

\(-10x + 10x - 6 = -6\)

We combine like terms on the left side:

\(-6 = -6\)

We notice that all variables dropped out.
We were solving for x, but there is no x in the equation anymore.
We also notice that we are left with the equation:

\(-6 = -6\)

which is true.

Since x dropped out of the equation leaving a true equation, that means no matter what x is the equation is true.

This means every value of x will work.
That means there is an infinite number of solutions.

Answer 13

When you get back, go over this. Then if you have any questions, just ask.