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!