Solve the following system of equations.
8x + 5y = -91
3x + y = -21
(-2,-15)
X=-2
Y=5
To solve the system of equations, we can use the method of substitution or the method of elimination. Here, we will use the method of substitution.
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the second equation for y in terms of x:
3x + y = -21
y = -3x - 21
Step 2: Substitute the expression for y from the second equation into the first equation.
8x + 5(-3x - 21) = -91
Step 3: Simplify and solve for x.
8x - 15x - 105 = -91
-7x - 105 = -91
-7x = -91 + 105
-7x = 14
x = 14 / -7
x = -2
Step 4: Substitute the value of x back into either of the original equations to solve for y.
Let's use the second equation:
3(-2) + y = -21
-6 + y = -21
y = -21 + 6
y = -15
Therefore, the solution to the system of equations is x = -2 and y = -15.