Question

8x + 5y=-22
-3x - 5y = 2

Answer 1

`x=-4,\:\\y=2`

Explanation:

`\begin{bmatrix}8x+5y=-22\\ -3x-5y=2\end{bmatrix}\\\mathrm{Multiply\:}8x+5y=-22\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:24x+15y=-66\\\mathrm{Multiply\:}-3x-5y=2\mathrm{\:by\:}8\:\mathrm{:}\:\quad \:-24x-40y=16\\\\\begin{bmatrix}24x+15y=-66\\ -24x-40y=16\end{bmatrix}\\\\-24x-40y=16\\+\\\underline{24x+15y=-66}\\-25y=-50\\\begin{bmatrix}24x+15y=-66\\ -25y=-50\end{bmatrix}\\-25y=-50\\\mathrm{Divide\:both\:sides\:by\:}-25\\(-25y)/(-25)=(-50)/(-25)\\y=2\\`

`\mathrm{For\:}24x+15y=-66\mathrm{\:plug\:in\:}y=2\\24x+15*\:2=-66\\24x+30=-66\\24x+30-30=-66-30\\24x=-96\\(24x)/(24)=(-96)/(24)\\x=-4\\\\\\x=-4,\:y=2`

Answer 2

(-4, 2).

Explanation:

8x + 5y=-22

-3x - 5y = 2 Adding the 2 equations:

5x = -20

x = -4.

Substitute x = -4 in the first equation:

8(-4) + 5y = -22

5y = -22 + 32

5y = 10

y = 2.