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

Answer:

x = 3, y = -1

Step-by-step 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:

$y=\frac{-19}{19}=-1$

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

$2x-3y=9\\2x-3(-1)=9\\2x+3=9\\2x=9-3=6\\x=\frac{6}{2}=3$