Question

Solve the following system of equations. y=-2x-9 2x 3y=-3 if there is one solution, type the answer as an ordered pair. if there is no solution, type ∅. if there are infinitely many solutions, type the answer as an equation in terms of x.

Answer 1

Solving the system of linear equations given, we found the ordered pair (-6, 3) as the solution by substituting the first equation into the second, simplifying, and then solving for x and y.

Step-by-step explanation:

To solve the system of equations y = -2x - 9 and 2x + 3y = -3, we can use substitution or elimination. Here, substitution is straightforward because the first equation explicitly defines y in terms of x.

By substituting the first equation into the second, we get:
2x + 3(-2x - 9) = -3
2x - 6x - 27 = -3
-4x - 27 = -3

Now, we solve for x:
-4x = -3 + 27
-4x = 24
x = -6

Substitute x back into the first equation to solve for y:
y = -2(-6) - 9
y = 12 - 9
y = 3

The solution to the system of equations is the ordered pair (-6, 3).