Question

Solve the system of equations algebraically.
5x - 3y = 6
6x - 4y = 2
a. many solutions
C.
no solution
b. (8, 14
d. (9. 13)
Please select the best answer from the choices provided
Ο Α
ОВ
О С

Answer 1

Answer:

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$x=9,\:y=13$

the option 'd' is correct.

Step-by-step explanation:

Given the system of the equations

$\begin{bmatrix}5x-3y=6\\ 6x-4y=2\end{bmatrix}$

$\mathrm{Multiply\:}5x-3y=6\mathrm{\:by\:}6\:\mathrm{:}\:\quad \:30x-18y=36$

$\mathrm{Multiply\:}6x-4y=2\mathrm{\:by\:}5\:\mathrm{:}\:\quad \:30x-20y=10$

$\begin{bmatrix}30x-18y=36\\ 30x-20y=10\end{bmatrix}$

$30x-20y=10$

$-$

$\underline{30x-18y=36}$

$-2y=-26$

$\begin{bmatrix}30x-18y=36\\ -2y=-26\end{bmatrix}$

solve for y

$-2y=-26$

$\mathrm{Divide\:both\:sides\:by\:}-2$

$\frac{-2y}{-2}=\frac{-26}{-2}$

$y=13$

$\mathrm{For\:}30x-18y=36\mathrm{\:plug\:in\:}y=13$

$30x-18\cdot \:13=36$

$30x-234=36$

$30x=270$

$\mathrm{Divide\:both\:sides\:by\:}30$

$\frac{30x}{30}=\frac{270}{30}$

$x=9$

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$x=9,\:y=13$

Therefore, the option 'd' is correct.