Question

One number is four more than five times another. If their sum is increased by one, the result is thirty-five. Find

the numbers.

Answer 1

29 and 5

Explanation:

Given system of equations

`\left \{ {{x=4+5y} \atop {x+y+1=35}} \right.`

Substitute top equation into bottom equation to determine y

`x+y+1=35\\\\(4+5y)+y+1=35\\\\4+5y+y+1=35\\\\5+6y=35\\\\6y=30\\\\y=5`

Substitute y=5 into top equation to determine the x-value

`x=4+5y\\\\x=4+5(5)\\\\x=4+25\\\\x=29`

Therefore, the two numbers are 29 and 5

Answer 2

x=4+5yif sum is increased by 3 (x+y+3), result is 31x+y+3=31minus 3 both sidesx+y=28x=4+5y subsiutute4+5y+y=284+6y=28minus 4 both sides6y=24divide by 6y=4sub backx=4+5yx=4+5(4)x=4+20x=24the numbers are 24 and 4

Explanation:

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