Notice that both equations coefficient of x" is "+1/2x is +12
This makes life easy as we can 'get rid' of one for the variables.
To solve an equation easily you need just one variable and a relationship to some constant.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given:
1/2x=y-112x=y−1............................(1)
1/2x+1/3y=512x+13y=5......................(2)
It is common practice to convert them so that they are of form
y=mx+cy=mx+c. This not strictly necessary in this case as the process will sort this out any way.
Equation (2) has the lesser value of yy so I am opting for:
color(brown)("Subtract equation (2) from equation (1) giving:")Subtract equation (2) from equation (1) giving:
color(green)("Notice how I have used 0 as a place keeper")Notice how I have used 0 as a place keeper
" "1/2x+0ycolor(white)(.)=y-1 12x+0y.=y−1
" "underline(1/2x+1/3y=0y+5 )->"subtract"
" "color(green)(0" " -1/3y=y-6)
Add color(magenta)(1/3y) to both sides
" "color(green)(-1/3ycolor(white)(.)color(magenta)(+1/3y)=ycolor(white)(.)color(magenta)(+1/3y)-6)
" "0=4/3y-6
Add 6 to both sides giving:
6=4/3y
color(blue)(y=(6xx3)/4 = 9/2)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I am choosing equation (1) for substitution of y
1/2x=y-1" "->" "1/2x=9/2-1
color(blue)(x=7)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check
1/2x+1/3y=5 " becomes "1/2(7)+1/3(9/2) = 5 Confirmed!
