Question

Which of the points is a solution to the following system of equations? -5x- 3/2y=15 3x+5/6 y=-44/3

Answer 1

Note: Your question sounds a little unclear, but I am assuming that your system of equations is:

`-5x-\:(3)/(2)y=15`

`3x+(5)/(6)y=-(44)/(3)`

• It would anyways clear your concept because the procedure to find the solutions remains the same for any set of a system of equations.

Answer:

The solution of the system of equations be:

`x=-(57)/(2),\:y=85`

Explanation:

Given the system of equations

`-5x-\:(3)/(2)y=15`

`3x+(5)/(6)y=-(44)/(3)`

solving the system of equations

`\begin{bmatrix}-5x-(3)/(2)y=15\\ 3x+(5)/(6)y=-(44)/(3)\end{bmatrix}`

`\mathrm{Multiply\:}-5x-(3)/(2)y=15\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:-15x-(9)/(2)y=45`

`\mathrm{Multiply\:}3x+(5)/(6)y=-(44)/(3)\mathrm{\:by\:}5\:\mathrm{:}\:\quad \:15x+(25)/(6)y=-(220)/(3)`

so the system of equations becomes

`\begin{bmatrix}-15x-(9)/(2)y=45\\ 15x+(25)/(6)y=-(220)/(3)\end{bmatrix}`

adding the equations

`15x+(25)/(6)y=-(220)/(3)`

`+`

`\underline{-15x-(9)/(2)y=45}`

`-(1)/(3)y=-(85)/(3)`

so

`\begin{bmatrix}-15x-(9)/(2)y=45\\ -(1)/(3)y=-(85)/(3)\end{bmatrix}`

solving
`-(1)/(3)y=-(85)/(3)` for y

`-(1)/(3)y=-(85)/(3)`

Multiply both sides by -3

`\left(-(1)/(3)y\right)\left(-3\right)=\left(-(85)/(3)\right)\left(-3\right)`

`y=85`

`\mathrm{For\:}-15x-(9)/(2)y=45\mathrm{\:plug\:in\:}y=85`

`-15x-(9)/(2)\cdot \:85=45`

`\mathrm{Add\:}(765)/(2)\mathrm{\:to\:both\:sides}`

`-15x-(765)/(2)+(765)/(2)=45+(765)/(2)`

`-15x=(855)/(2)`

`\mathrm{Divide\:both\:sides\:by\:}-15`

`(-15x)/(-15)=((855)/(2))/(-15)`

`x=-(57)/(2)`

Therefore, the solution of the system of equations be:

`x=-(57)/(2),\:y=85`