Question

3x-2y=2, 5x-5y=-18
Solve by elimination

Answer 1

5(3x-2y=2)

15x -10y = 10

2(5x-5y=-18)

10x - 10y = -36
- 15x - 10y = 10

-5x = 46
/-5 /-5

x = 9.2

3(9.2) - 2y = 2

27.6 - 2y = 2
-27.6 -27.6

-2y = 25.6
/-2 /-2

y = 12.8

x = 9.2; y = 12.8

Answer 2

We have
`\begin{bmatrix}3x-2y=2\\ 5x-5y=-18\end{bmatrix}`


`\mathrm{Multiply\:}3x-2y=2\mathrm{\:by\:}5:\quad 15x-10y=10`

`\mathrm{Multiply\:}5x-5y=-18\mathrm{\:by\:}3:\quad 15x-15y=-54`


`\begin{bmatrix}15x-10y=10\\ 15x-15y=-54\end{bmatrix}`

15x - 15y = -54
-
15x - 10y = 10
/
-5y = -64


`\begin{bmatrix}15x-10y=10\\ -5y=-64\end{bmatrix}`


`-5y=-64 \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}-5 \ \textgreater \ (-5y)/(-5)=(-64)/(-5) \ \textgreater \ y=(64)/(5)`


`\mathrm{For\:}15x-10y=10\mathrm{\:plug\:in\:}\ \:y=(64)/(5)`


`15x-10\cdot (64)/(5)=10 \ \textgreater \ 10\cdot (64)/(5) \ \textgreater \ \mathrm{Multiply\:fractions}:\ \:a\cdot (b)/(c)=(a\:\cdot \:b)/(c)`


`(64\cdot \:10)/(5) \ \textgreater \ \mathrm{Multiply\:the\:numbers:}\:64\cdot \:10=640 \ \textgreater \ (640)/(5)`


`\mathrm{Divide\:the\:numbers:}\:(640)/(5)=128 \ \textgreater \ 15x-128=10`


`\mathrm{Add\:}128\mathrm{\:to\:both\:sides} \ \textgreater \ 15x-128+128=10+128 \ \textgreater \ 15x=138`


`\mathrm{Divide\:both\:sides\:by\:}15 \ \textgreater \ (15x)/(15)=(138)/(15) \ \textgreater \ x=(46)/(5)`


`Therefore\:the\:solutions\:are \ \textgreater \ y=(64)/(5),\:x=(46)/(5)`