One number is 4 less than -> n_1=?-4→n1=?−4
3 times " ........................."->n_1=3?-4 .........................→n1=3?−4
the second number color(brown)(".........."->n_1=3n_2-4)..........→n1=3n2−4
color(white)(2/2)22
If 3 more " ..........................................."-> ?+3 ...........................................→?+3
than two times the first number" ............"->2n_1+3 ............→2n1+3
is decreased by "..................................."->2n_1+3-?...................................→2n1+3−?
2 times the second number" ................."->2n_1+3-2n_2 .................→2n1+3−2n2
the result is 11color(brown)(" ....................................."->2n_1+3-2n_2=11) .....................................→2n1+3−2n2=11
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(white)(.)n_1=3n_2-4.n1=3n2−4 .....................Equation (1)
2n_1+3-2n_2=112n1+3−2n2=11...........Equation (2)
Substitute for n_1n1 in equation (2) using equation (1)
color(brown)(2n_1+3-2n_2=11)" "color(blue)( ->2(3n_2-4)+3-2n_2=11)2n1+3−2n2=11 →2(3n2−4)+3−2n2=11
Multiplying out the brackets
6n_2-8+3-2n_2=116n2−8+3−2n2=11
4n_2-5=114n2−5=11
Add 5 to both sides
4n_2=164n2=16
Divide both sides by 4
" "color(green)(n_2=4) n2=4
;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute n_2=4n2=4 into equation (1)
n_1=3(4)-4n1=3(4)−4
n_1=12-4n1=12−4
" "color(green)(n_1=8) n1=8
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check: One number is 4 less than 3 times the second number
8=3(4)-4=88=3(4)−4=8 confirmed!
