Solve using the substitution method.
-$$\begin{array} { l }
x + y = 16 \
y = 3 x + 4
\end{array}$$
A) $( 4,12 )$
B) $( 2,16 )$
C) $( 3,13 )$
D) $( 13,3 )$

Question

Solve using the substitution method.
-$$\begin{array} { l } 
x + y = 16 \
y = 3 x + 4
\end{array}$$
A) $( 4,12 )$
B) $( 2,16 )$
C) $( 3,13 )$
D) $( 13,3 )$

Quizplus · Accepted Answer

We can use the second equation, y=3x+4, to substitute for y in the first equation.

Substitute y=3x+4 into x+y=16:

x + (3x+4) = 16

Simplify the equation:

4x+4 = 16

Subtract 4 from both sides:

4x = 12

Divide by 4:

x = 3

Now that we know x=3, we can substitute it back into either equation to solve for y.

Using y=3x+4:

y=3(3)+4

y=13

Therefore the solution is (3,13) which corresponds to Choice C.

Solve Using the Substitution Method x+y=16y=3x+4\begin{array} { l } x + y = 16 \\y = 3 x + 4\end{array}x+y=16y=3x+4​

Solve Using the Substitution Method $\begin{array} { l } x + y = 16 \\y = 3 x + 4\end{array}$