what is the solution to the system containing the equation ? x + y = -8 and -3x + 2y = 9
Multiply first equation by 3.
3x + 3y = -24
-3x + 2y = 9
Add the two equations.
5y = -15
y = -3
Put y value in one equation.
x + (-3) = -8
x = -5
Check by putting both values in the other equation.
(-3)(-5) + 2(-3) = 9
15-6 = 9
To find the solution to the given system of equations, we can use the method of substitution or elimination. I will use the method of substitution to explain it step by step:
Step 1: Solve one equation for one variable in terms of the other variable. Let's solve the first equation, x + y = -8, for x:
x = -8 - y
Step 2: Substitute the expression we found for x into the second equation, -3x + 2y = 9:
-3(-8 - y) + 2y = 9
Step 3: Simplify the equation:
24 + 3y + 2y = 9
5y + 24 = 9
Step 4: Subtract 24 from both sides of the equation:
5y = 9 - 24
5y = -15
Step 5: Divide both sides of the equation by 5:
y = -15/5
y = -3
Step 6: Substitute the value we found for y back into the first equation, x + y = -8, to solve for x:
x + (-3) = -8
x - 3 = -8
x = -8 + 3
x = -5
Therefore, the solution to the given system of equations is x = -5 and y = -3.