If 2x + 2y = 20
&
5x - 3y = 15
Solve using the substitution method.
from eq #1, you know y = 10-x
substitute that into eq #2 and you have
5x-3(10-x) = 15
Now you can find x, and then y.
x=5.625 y=4.375
I have been reworking this problem since last night, even using y=10-x, and was still coming up with incorrect answers. Thank you!
To solve the system of equations using the substitution method, we need to isolate one variable in one equation and then substitute it into the other equation.
Let's start by isolating one variable in the first equation. We can choose to isolate x or y. In this case, let's isolate x in the first equation.
2x + 2y = 20
To isolate x, subtract 2y from both sides of the equation:
2x = 20 - 2y
Next, divide both sides of the equation by 2 to solve for x:
x = (20 - 2y) / 2
Now we have an expression for x in terms of y. We will substitute this expression for x into the second equation.
5x - 3y = 15
Replace x with (20 - 2y) / 2 in the second equation:
5((20 - 2y) / 2) - 3y = 15
Now we can simplify this equation:
10 - 2y - 3y = 15
Combine like terms:
-5y = 5
To solve for y, divide both sides of the equation by -5:
y = -5 / -5
y = 1
Now that we have the value for y, we can substitute it back into the first equation to solve for x.
2x + 2(1) = 20
2x + 2 = 20
Subtract 2 from both sides:
2x = 18
Divide both sides of the equation by 2:
x = 18 / 2
x = 9
Therefore, the solution to the system of equations is x = 9 and y = 1.