Question

Find the points of intersection of the lines 10x−4y=2 and 2x+8y=7 without graphing.

Answer 1

`x=(1)/(2),y=(3)/(4)`

Explanation:

Given:

`10x-4y=2 ,2x+8y=7`

To find: points of intersection of the given lines

Solution:

In substitution method, the system of equations is solved by expressing one variable in terms of another, as a result, removing one variable from an equation.

`10x-4y=2 \\2(5x-2y)=2\\5x-2y=1\\5x=1+2y\\x=(1+2y)/(5)`

Put
`x=(1+2y)/(5)` in the equation
`2x+8y=7`

`2x+8y=7\\2[(1+2y)/(5)]+8y=7\\ 2+4y+40y=35\\44y=35-2\\44y=33\\y=(33)/(44)\\ =(3)/(4)`

Put
`y=(3)/(4)` in the equation
`x=(1+2y)/(5)`

`x=(1+2y)/(5)\\=(1)/(5)[1+2((3)/(4))]\\=(1)/(5)[1+((3)/(2))]\\\\=(1)/(5)((2+3)/(2)) \\\\=(1)/(5)((5)/(2))\\\\=(1)/(2)`

Therefore,

`x=(1)/(2),y=(3)/(4)`