find the values ofx and y that solve the following system of equations
-3x- 8y=19
4x+9y=-22
To solve the given system of equations:
Step 1: Choose one of the equations and solve for one variable in terms of the other variable.
Let's solve the first equation for x:
-3x - 8y = 19
-3x = 19 + 8y
x = (19 + 8y) / -3
Step 2: Substitute the value of x obtained in the previous step into the other equation and solve for y.
Substituting x in the second equation:
4x + 9y = -22
4((19 + 8y) / -3) + 9y = -22
(76 + 32y) / -3 + 9y = -22
Multiply through by -3 to eliminate fractions:
76 + 32y - 27y = -66
76 + 5y = -66
5y = -66 - 76
5y = -142
y = -142 / 5
y = -28.4
Step 3: Substitute the value of y back into the equation we obtained in step 1 and solve for x.
x = (19 + 8y) / -3
x = (19 + 8(-28.4)) / -3
x = (19 - 227.2) / -3
x = -208.2 / -3
x = 69.4
So the solution to the system of equations is x = 69.4 and y = -28.4.