Question

Use the substitution method to solve the system 2.5x+y=-2, 3x+2y=0 (1 point) Infinite solutions no solution (-2,3) (3,-2)

Answer 1

To solve the system using the substitution method, we'll start by solving one equation for one variable and substituting it into the other equation.

Let's solve the first equation, 2.5x + y = -2, for y:

y = -2 - 2.5x

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

3x + 2(-2 - 2.5x) = 0

Simplify this equation:

3x - 4 - 5x = 0

Combine like terms:

-2x - 4 = 0

Add 4 to both sides:

-2x = 4

Divide both sides by -2:

x = -2

Now substitute this value of x into the first equation to solve for y:

2.5(-2) + y = -2

-5 + y = -2

Add 5 to both sides:

y = 3

Therefore, the solution to the system of equations is (x, y) = (-2, 3).