Question

4x-12y= 13
32y+14x=13

Answer 1

x = 143/74

y = -65/148

Explanation:

4x-12y= 13

4x = 13 + 12y

x = 13/4 + 3y

32y+14x=13

32y + 14(13/4 + 3y) = 13

32y + 91/2 + 42y = 13

74y = 13 - 91/2

74y = -65/2

y = -65/148

x = 13/4 + 3(-65/148)

x = 143/74

x = 143/74

y = -65/148

Answer 2

(143/74, -65/148)

Explanation:

We have the equations:

4x - 12y = 13

14x + 32y = 13

Let's use elimination, so multiply the first equation by 8 and the second equation by 3:

8 * (4x - 12y = 13) ⇒ 32x - 96y = 104

3 * (14x + 32y = 13) ⇒ 42x + 96y = 39

Add those two equations:

32x - 96y = 104

+ 42x + 96y = 39

________________

74x + 0y = 143

Divide both sides by 74:

x = 143/74

Plug this into an equation to find y:

4x - 12y = 13

4 * (143/74) - 12y = 13

12y = 572/74 - 13 = -390/74

y = -65/148

The answer is (143/74, -65/148).