y = 4x - 6
2x - 3y = 8
If this problem is to be solved by substitution, which is a correct step?
Responses
A 2x - 12x + 18 = 8
B 2x - 12x - 18 = 8
C 2x - 4x + 6 = 8
D 2x + 12x + 18 = 8
To solve the system of equations using substitution, first solve one equation for one variable and substitute it into the other equation.
Let's solve the first equation for x:
y = 4x - 6
Add 6 to both sides:
y + 6 = 4x
Divide both sides by 4:
x = (y + 6)/4
Now substitute this expression for x into the second equation:
2x - 3y = 8
2((y + 6)/4) - 3y = 8
Simplify:
(y + 6)/2 - 3y = 8
To continue solving the system of equations by substitution, we need to simplify and rearrange this equation. None of the options provided match this step, so none of the options are correct.
one of the options IS correct
Apologies for the mistake. Let's re-evaluate the options:
A) 2x - 12x + 18 = 8
B) 2x - 12x - 18 = 8
C) 2x - 4x + 6 = 8
D) 2x + 12x + 18 = 8
Now we'll substitute the value of x from the first equation (x = (y + 6)/4) into the second equation (2x - 3y = 8) to find the correct option.
Substituting, we have:
2((y + 6)/4) - 3y = 8
Simplifying:
(y + 6)/2 - 3y = 8/1
Multiplying both sides by 2 to clear the fraction:
(y + 6) - 6y = 16
Simplifying further:
y + 6 - 6y = 16
-5y + 6 = 16
Now, let's check which option matches this step:
A) 2x - 12x + 18 = 8 - This option doesn't match the current step since it has different numbers.
B) 2x - 12x - 18 = 8 - This option also doesn't match the current step.
C) 2x - 4x + 6 = 8 - This option matches the current step.
D) 2x + 12x + 18 = 8 - This option also doesn't match the current step.
Therefore, option C) 2x - 4x + 6 = 8 is the correct step for solving the system of equations using substitution.