If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the first equation is substituted into the second equation.
x – 2y = 2
x + 3y = 17
in the first equation x=2+2y
now into the second
2+2y + 3y=17 TaDa!
To solve the system of equations using the substitution method, we need to isolate one variable in one of the equations and substitute this expression into the other equation.
Let's start by isolating x in the first equation:
x - 2y = 2
Adding 2y to both sides, we have:
x = 2y + 2
Now, we can substitute this expression for x into the second equation:
x + 3y = 17
Replace x with 2y + 2:
(2y + 2) + 3y = 17
Simplify:
5y + 2 = 17
To solve for y, subtract 2 from both sides:
5y = 15
Now, divide both sides by 5 to solve for y:
y = 3
Now that we have found the value of y, we can substitute it back into one of the original equations to find x. Let's use the first equation:
x - 2(3) = 2
x - 6 = 2
To solve for x, add 6 to both sides:
x = 8
Therefore, the solution to the system of equations is x = 8 and y = 3.
To answer your original question, after substituting x = 2y + 2 into the second equation x + 3y = 17, the new equation is (2y + 2) + 3y = 17.