Question

Solve the simultaneous equation:
5 x + 2 y = 25
5 x − y = 10

Answer 1

x= 3 y= 5

Explanation:

5x+ 2y=25

5x-y=10

therefore 2(5x-y=10)

10x-2y=20

equation 2÷ eqation1

we get 15x=45

x=3

y=5

Answer 2

(x, y) = (3, 5)

Explanation:

`5x+2y=25\\5x-y=10`

Solving by elimination here again, there are 2 good options available. Either multiply the whole bottom equation by -1 to cancel the x, or by 2 to cancel the y. I'll do the latter:

`5x+2y=25\\\\2(5x-y=10)\\10x-2y=20`

Add from top to bottom:

`\rightarrow (5x+10x)+(2y-2y)=25+20\\\rightarrow 15x=45\\\rightarrow x=3`

Now, with the value of x, solve for y in either of the equations. I'll choose the second one here:

`\rightarrow 5x-y=10\\\rightarrow 5(3)-y=10\\\rightarrow 15-y=10\\\rightarrow -y=-5\\\rightarrow y=5`

(x, y) = (3, 5)