What is the solution to the system of equations?

Use any method.

2x-3y=9

3x+5y=4

x = 3 and y = - 1

Step-by-step explanation:

To solve a system of equations, use graphing, substitution, or elimination. Here we use substitution. In substitution, solve one equation for a variable. Then substitute the equation into another equation. this creates an equation in one variable. Then solve for the variable.

Solve 2x - 3y = 9 for x.

2x - 3y = 9

2x = 9 + 3y

x = 9/2 + 3/2y

Substitute this equation into 3x + 5y = 4.

3 (9/2+3/2y) + 5y = 4

27/2 + 9/2 y + 5y = 4

Clear the fractions by multiplying everything by 2.

27 + 9y + 10y = 8

27 + 19y = 8

19y = - 19

y = - 1

Substitute y = - 1 into 2x - 3y = 9 to solve for x.

2x - 3 (-1) = 9

2x + 3 = 9

2x = 6

x = 3