Which of the following choices constitutes a simultaneous solution to these equations? $$\begin{array} { l }
3 \mathrm { x } + 4 \mathrm { y } = 10 \
5 \mathrm { x } + 4 \mathrm { y } = 14
\end{array}$$
A) x = 2, y = .5
B) x = 4, y = -.5
C) x = 2, y = 1
D) x = y
E) y = 2x

Question

Which of the following choices constitutes a simultaneous solution to these equations? $$\begin{array} { l } 
3 \mathrm { x } + 4 \mathrm { y } = 10 \
5 \mathrm { x } + 4 \mathrm { y } = 14
\end{array}$$
A) x = 2, y = .5
B) x = 4, y = -.5
C) x = 2, y = 1
D) x = y
E) y = 2x

Quizplus · Accepted Answer

To find the solution to the system of equations, we can use either elimination or substitution. One way to approach the problem is to use elimination. We can eliminate y by multiplying the first equation by −1 and adding the resulting equation to the second equation, creating a new equation with only x:

$$\begin{array} { l } 
3 \mathrm { x } + 4 \mathrm { y } = 10 \
(-1)\cdot(3 \mathrm { x } + 4 \mathrm { y })=(-1)\cdot(10)\longrightarrow -3 \mathrm { x } - 4 \mathrm { y } = -10 \
5 \mathrm { x } + 4 \mathrm { y } = 14\
\hline \
2 \mathrm { x }=4 \
\end{array}$$

Solving for x, we get x=2. We can substitute this value of x into either equation to find y. Using the first equation:

$$3 \cdot 2+4y = 10$$
$$6+4y =10$$
$$4y=4$$
$$y=1$$

Therefore, the simultaneous solution to the system of equations is x=2 and y=1, which is answer choice C.

Which of the Following Choices Constitutes a Simultaneous Solution to These