Question

Solve the following pairs of simultaneous equations

a) x + 3y = 14
3x + y = 10

b) 5x + y = 27
4x + 3y = 26

c) -6x + 5y = -14
-2x + y = -6

d) 2x + 5y = 14
3x + y = -5

e) -3x + 2y = 6
x + 4y = -9

f) 3x - 5y = 7
x + y = -11

g) 2x + 3y = 9
4x + y = -7

h) -x +5y = 7
5x + 5y = 19

Answer 1

a)

`x + 3y = 14|\cdot(-3)\\3x + y = 10\\\\-3x - 9y = -42\\3x + y = 10\\\\-8y = -32 => y = 4, x = 14 - 12 = 2\\(2, 4)`

b)

`5x + y = 27|\cdot(-3)\\4x + 3y = 26\\\\-15x - 3y = -81\\4x + 3y = 26\\\\-11x = - 55 => x=5, y = 27-25 = 2\\(5, 2)`

c)

`-6x + 5y = -14\\-2x + y = -6| \cdot(-3)\\\\-6x + 5y = -14\\6x - 3y = 18\\\\2y = 4 => y = 2, x = -1/2\cdot(-6 -2) = 4\\(4, 2)`

d)

`2x + 5y = 14\\3x + y = -5|\cdot(-5)\\\\2x + 5y = 14\\-15x - 5y = 25\\\\-13x = 39 => x = -3, y = 1/5\cdot(14 - 2(-3)) = 4\\(-3, 4)`

e)

`-3x + 2y = 6\\x + 4y = -9|\cdot3\\\\-3x + 2y = 6\\3x + 12y = -27\\\\14y = -21 => y = -(3)/(2), x = -3\\(-3, -1.5)`

f)

`3x - 5y = 7\\x + y = -11|\cdot(5)\\\\3x - 5y = 7\\5x + 5y = -55\\\\8x = -48=> x= -6, y = -11 + 6 = -5\\(-6, -5)`

g)

`2x + 3y = 9|\cdot(-2)\\4x + y = -7\\\\-4x - 6y = -18\\4x + y = -7\\\\-5y = -25 => y = 5, x = 1/4(-7-5) = -3\\(-3, 5)`

h)

`-x + 5y = 7|\cdot(-1)\\5x + 5y = 19\\\\x-5y = -7\\5x + 5y = 19\\\\6x = 12 => x = 2, y = (7 + 2)/5 = (9)/(5)\\(2, 1.8)`