Question

How do you solve 7x - 2y = 4 and 5y + 3x = 10?

Answer 1

point of intersection`->(x,y)=(40/41,58/41)`

Explanation:

`color(blue)("Using first principles")`

There are various ways of solving this question type. What follows is just one of them.

Given:
`7x-2y=4` ...............................Equation(1)
`5y+3x=10` ............................Equation(2)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the value of "x)`

Consider equation (2)

Subtract `3x` from both sides giving:

`5y=10-3x`

Divide both sides by 5

`y=10/5-3/5x` ..............................Equation(3)
,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Using equation(3) substitute for y in equation (1)

`color(brown)(7x-2y=4)color(blue)(" "->" "7x-2(10/5-3/5x)=4`

`=>7x-4+6/5x=4`

`41/5x-4=4`

Add 4 to both sides

`41/5x=8`
Multiply both sides by `5/41`

`color(blue)(=>x=5/41xx8" " =" "40/41)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the value of ")`
`color(brown)("Using shortcuts method")`
Substitute `x=40/41` into equation(2)

`color(brown)(5y+3x=10color(blue)(" "->" "5y+3(40/41)=10))`

`y=58/41`