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# ​2+2

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2x+3y=13
12x-3y=-2

Sep 29, 2017

### 2+0 Answers

#1
+1

Solve the following system:
{2 x + 3 y = 13 | (equation 1)
12 x - 3 y = -2 | (equation 2)

Swap equation 1 with equation 2:
{12 x - 3 y = -2 | (equation 1)
2 x + 3 y = 13 | (equation 2)

Subtract 1/6 × (equation 1) from equation 2:
{12 x - 3 y = -2 | (equation 1)
0 x+(7 y)/2 = 40/3 | (equation 2)

Multiply equation 2 by 6:
{12 x - 3 y = -2 | (equation 1)
0 x+21 y = 80 | (equation 2)

Divide equation 2 by 21:
{12 x - 3 y = -2 | (equation 1)
0 x+y = 80/21 | (equation 2)

Add 3 × (equation 2) to equation 1:
{12 x+0 y = 66/7 | (equation 1)
0 x+y = 80/21 | (equation 2)

Divide equation 1 by 12:
{x+0 y = 11/14 | (equation 1)
0 x+y = 80/21 | (equation 2)

x = 11/14               and                      y = 80/21

Sep 29, 2017
#2
+1

2x+3y=13  ⇒   3y   = 13 - 2x      (1)
12x-3y=-2 ⇒    3y  =   2 + 12x    (2)

Set (1)  = (2)

13 - 2x  =  2 + 12x     add 2x to both sides, subtract 2 from  both sides

11   = 14x         divide both sides by 14

11/ 14  = x

Putting this into (1), we have

3y  = 13 - 2 (11/ 14)

3y  = 13  - 11/7           get a common denominator

3y  = 91/7 - 11/7

3y  = 80/7          divide both sides by 3

y  = 80/ 21   Sep 29, 2017