Solve the system of equations using substitution, elimination by addition, or augmented

matrix methods (your choice). Show work.
3๐‘ฅ โˆ’ 2๐‘ฆ = 5
5๐‘ฅ + 3๐‘ฆ = 21

Multiply Eq1 by 3 and Eq2 by 2:

9x - 6y = 15.
10x + 6y = 42.
Solve by addition.

To solve the system of equations using the elimination by addition method, we will eliminate one variable by adding the two equations together.

First, let's solve either equation for one variable in terms of the others. Let's solve the first equation for x:

3x - 2y = 5

Add 2y to both sides:

3x = 2y + 5

Divide both sides by 3:

x = (2y + 5)/3

Now, substitute this expression for x into the second equation:

5(2y + 5)/3 + 3y = 21

Simplify the equation:

(10y + 25)/3 + 3y = 21

Multiply every term in the equation by the common denominator, which is 3:

10y + 25 + 9y = 63

Combine like terms:

19y + 25 = 63

Subtract 25 from both sides:

19y = 38

Divide both sides by 19:

y = 2

Now that we have the value of y, substitute it back into the first equation to find the value of x:

3x - 2(2) = 5

Simplify the equation:

3x - 4 = 5

Add 4 to both sides:

3x = 9

Divide both sides by 3:

x = 3

Therefore, the solution to the system of equations is x = 3 and y = 2.