One number is 4 less than 3 times a second number. If 3 more than two times the first number is decreased by 2 times the second number, the result is 11. Use the substitution method. What is the first number?

One number is 4 less than #-> n_1=?-4#
3 times #" ........................."->n_1=3?-4#
the second number #color(brown)(".........."->n_1=3n_2-4)#
#color(white)(2/2)#

If 3 more #" ..........................................."-> ?+3#
than two times the first number#" ............"->2n_1+3#
is decreased by #"..................................."->2n_1+3-?#
2 times the second number#" ................."->2n_1+3-2n_2#
the result is 11#color(brown)(" ....................................."->2n_1+3-2n_2=11)#

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#color(white)(.)n_1=3n_2-4# .....................Equation (1)
#2n_1+3-2n_2=11#...........Equation (2)

Substitute for #n_1# in equation (2) using equation (1)

#color(brown)(2n_1+3-2n_2=11)" "color(blue)( ->2(3n_2-4)+3-2n_2=11)#

Multiplying out the brackets

#6n_2-8+3-2n_2=11#

#4n_2-5=11#

Add 5 to both sides

#4n_2=16#

Divide both sides by 4

#" "color(green)(n_2=4)#
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Substitute #n_2=4# into equation (1)

#n_1=3(4)-4#

#n_1=12-4#

#" "color(green)(n_1=8)#
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Check: One number is 4 less than 3 times the second number

#8=3(4)-4=8# confirmed!