Solve the system by using the substitution method. $$\left( \begin{array} { c }
3 x + y = 17 \
4 x - y = 18
\end{array} \right)$$
A) (5, 32)
B) (2, 5)
C) (5, 2)
D) no solutions
E) infinitely many solutions

Question

Solve the system by using the substitution method. $$\left( \begin{array} { c } 
3 x + y = 17 \
4 x - y = 18
\end{array} \right)$$
A) (5, 32)
B) (2, 5)
C) (5, 2)
D) no solutions
E) infinitely many solutions

Quizplus · Accepted Answer

From the first equation, we can solve for y:
$$ y = 17 - 3x $$

Substitute this expression for y into the second equation:
$$ 4x - (17-3x) = 18 $$

Simplifying, we get:
$$ 7x = 35 $$

Solving for x, we get:
$$ x = 5 $$

Now that we know x, we can substitute it back into either of the original equations to solve for y. Using the first equation:
$$ 3(5) + y = 17 $$

Solving for y, we get:
$$ y = 2 $$

Therefore, the solution to the system is (5,2).

Solve the System by Using the Substitution Method (3x+y=174x−y=18)\left( \begin{array} { c } 3 x + y = 17 \\4 x - y = 18\end{array} \right)(3x+y=174x−y=18​)

Solve the System by Using the Substitution Method $\left( \begin{array} { c } 3 x + y = 17 \\4 x - y = 18\end{array} \right)$