31.0k views
4 votes
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

1 Answer

2 votes

Answer:


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


x=9,\:y=13

the option 'd' is correct.

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


(-2y)/(-2)=(-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


(30x)/(30)=(270)/(30)


x=9


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


x=9,\:y=13

Therefore, the option 'd' is correct.