Solve by the substitution method.
7x + 2y = -19
-5x + y = 33
What is the solution of the system?
(Type an ordered pair.)
-5x + y = 33 ---> y = 5x + 33
now sub that into the first equation
7x + 2y = -19
7x + 2(5x + 33) = -19
solve for x, then sub that into y = 5x + 33 to get y
To solve the system of equations using the substitution method, we need to solve one equation for one variable and substitute that expression into the other equation.
Let's solve the second equation for y:
-5x + y = 33
Rearranging the equation, we have:
y = 5x + 33
Now, substitute this expression for y in the first equation:
7x + 2(5x + 33) = -19
Simplify the equation:
7x + 10x + 66 = -19
Combine like terms:
17x + 66 = -19
Now, solve for x:
17x = -19 - 66
17x = -85
Divide both sides by 17:
x = -85 / 17
x = -5
Now substitute the value of x back into one of the original equations to solve for y. Let's use the second equation:
-5(-5) + y = 33
25 + y = 33
Subtract 25 from both sides:
y = 33 - 25
y = 8
So the solution to the system of equations is (x, y) = (-5, 8).