Question

What is the solution to the system of equations?

Use any method.
{2x−3y=9
{3x+5y=4
Enter your answer in the boxes. Parentheses are already provided.

Answer 1

x = 3, y = -1

Explanation:

The system of equations to solve is:

`2x-3y=9\\3x+5y=4`

We proceed as follows:

1) First of all, we multiply equation (1) by 3, and we get:

`6x-9y=27` (1)

2) Then, we multiply equation (2) by 2, and we get:

`6x+10y=8` (2)

3) Now we notice that the coefficient of the variable x is the same in the 2 equations; so, we subtract eq(1) from eq(2), and we get:

`(6x-6x)+(10y-(-9y))=8-27\\19y=-19`

4) We solve this equation for y, and we get:

`y=(-19)/(19)=-1`

5) We substitute this value of y back into the original equation (1), and we solve for x:

`2x-3y=9\\2x-3(-1)=9\\2x+3=9\\2x=9-3=6\\x=(6)/(2)=3`