Solve the following system of equations. Explain which method you used and why you chose that method
10x-6y=2
5x+3y=5

Question

Solve the following system of equations. Explain which method you used and why you chose that method
10x-6y=2
5x+3y=5

mathstudent55 · Answer

I have a suggestion.
The addition method is practical to use when, by adding the equations, a variable is eliminated.

mathstudent55 · Answer

That can be done easily here.
Notice the first equation has the term -6y and the second equation has the term 3y.
If you turn the term 3y of the second equation into 6y, then adding those terms would eliminate y, since 6y + (-6y) = 0.
Since you need 6y in the second equation, multiply the entire second equation by 2.
Then add the equations together.

mathstudent55 · Answer

Copy the first equation exactly as it is.
Below it, write the second equation multiplied by 2.
Then add the two equations.

anonymous · Answer

what about 2 and 5, do I add both of them together too?

mathstudent55 · Answer

Yes, but remember that the 5 becomes 10 when you multiply the second equation by 2.
I'll show it to you below.

Here is the original system of equations:
$10x-6y=2 $
$5x+3y=5$

Now we copy the first equation as it is.
Below it, we write the second equation after multiplying it by 2 on both sides.

$10x-6y=2 $
$10x+6y=10$

Now we add the two equations:

$20x + 0y = 12$

$20x = 12$

Now that we have one equation in one variable, x, we solve for the variable.

Divide both sides by 20:

$\dfrac{20}{20}x = \dfrac{12}{20}$

Reduce the fraction by dividing the numerator and denominator by 5.

$x = \dfrac{3}{5} $

Now that we have x, we can use the equations to eliminate x and solve for y.
Let's go back to the step where the second equation had been multiplied by 2.

The two equations are (copied form above):

$10x-6y=2 $
$10x+6y=10$

Now we subtract the equations. The terms 10x in both equations will be eliminated leaving an equation in only y.

Subtracting the equations we get:

$-12y = -8$

Divide both sides by -12 and reduce the fration:

$\dfrac{-12}{-12}y = \dfrac{-8}{-12}$

$y = \dfrac{8}{12} $

$y = \dfrac{2}{3} $

The solution is:  $x = \dfrac{3}{5} $,    $y = \dfrac{2}{3} $