Question

Use the substitution method to solve the system 2.5x+y=−2 , 3x+2y=0 .

no solution

infinite solutions

(−2,3)

(3,−2)

Answer 1

To solve the system using the substitution method, we can solve one equation for one variable and substitute it into the other equation.

Let's solve the first equation for y:

2.5x + y = -2
y = -2 - 2.5x

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

3x + 2(-2 - 2.5x) = 0
3x - 4 - 5x = 0
-2x - 4 = 0
-2x = 4
x = -2

Now substitute x = -2 back into the first equation to solve for y:

2.5(-2) + y = -2
-5 + y = -2
y = -2 + 5
y = 3

Therefore, the solution to the system of equations is (−2,3).