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

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

$-5y=-64 \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}-5 \ \textgreater \ \frac{-5y}{-5}=\frac{-64}{-5} \ \textgreater \ y=\frac{64}{5}$

$\mathrm{For\:}15x-10y=10\mathrm{\:plug\:in\:}\ \:y=\frac{64}{5}$

$15x-10\cdot \frac{64}{5}=10 \ \textgreater \ 10\cdot \frac{64}{5} \ \textgreater \ \mathrm{Multiply\:fractions}:\ \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}$

$\frac{64\cdot \:10}{5} \ \textgreater \ \mathrm{Multiply\:the\:numbers:}\:64\cdot \:10=640 \ \textgreater \ \frac{640}{5}$

$\mathrm{Divide\:the\:numbers:}\:\frac{640}{5}=128 \ \textgreater \ 15x-128=10$

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

$\mathrm{Divide\:both\:sides\:by\:}15 \ \textgreater \ \frac{15x}{15}=\frac{138}{15} \ \textgreater \ x=\frac{46}{5}$

$Therefore\:the\:solutions\:are \ \textgreater \ y=\frac{64}{5},\:x=\frac{46}{5}$