Solve the system using substitution.
x = y − 6
y = 6 − 3x
A. (0, 6)
B. (6, 0)
C. (0, −6)
D. (−6, 0)
To solve the system of equations using substitution, we will solve one equation for one variable and substitute its value into the other equation.
Let's solve the first equation, x = y - 6, for x:
x = y - 6
Now, substitute this value of x into the second equation, y = 6 - 3x:
y = 6 - 3(x)
Substituting the value of x, we get:
y = 6 - 3(y - 6)
Simplifying further:
y = 6 - 3y + 18
y = -3y + 24
4y = 24
y = 6
Now, substitute this value of y back into the first equation to find x:
x = y - 6
x = 6 - 6
x = 0
Therefore, the solution to the system of equations is (x, y) = (0, 6).
So, the correct answer is A. (0, 6).
well, geez -- how about, um, substituting?
You see that x = y-6, so substitute that into the other equation and you can then find y:
y = 6-3(y-6)
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