Question

Question #2d385

Answer 1

First part in a lot of detail to demonstrate algebraic manipulation.
Second part not so.

Point common to both equations is:
`(x,y)->(3,2)`

Explanation:

Given:`" "7x+y=23` ........................Equation (1)
`" "3x=4y+1`.........................Equation (2)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider equation(1)

Subtract `7x` from both sides

`y=-7x+23" ............................Equation" (1_a)`

`color(green)("Substitute for "color(blue)(y)" in equation (2) using "(1_a))`

`color(brown)(3x=4color(blue)(y)+1" "->" "3x=4color(blue)((-7x+23))+1)`

`color(white)()`

`color(brown)(3x=-28x+92+1)" "color(green)(larr" multiplied out the bracket")`
`color(white)()`

`color(brown)(3xcolor(blue)(+28x)=-28xcolor(blue)(+28x)+93)color(green)(larr" add "color(blue)(28x)" to both sides")`
`color(white)()`

`color(brown)(31x=0+93)`
`color(white)()`

`color(brown)(31/(color(blue)(31)) x=93/(color(blue)(31)) )color(green)(larr" divide both sides by "color(blue)(31))`

`color(white)()`

`color(brown)(x=3)" "color(green)(larr31/31=1" and "93/31 = 3)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute for `x` in (1)

`7x+y=23" " =>" " y=2`