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

`\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.