Question

The sum of two number is 10.If their sum is five times their difference,find the numbers.

Answer 1

Heye

your answer ⏬

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★ we know that,

X + Y = 10

X + Y = 10X - 5Y = 20

X + Y = 10X - 5Y = 20Now you need to add the equations together to solve for one variable. I will multiply both sides of the bottom equation by -1 so that the X variable cancels (as long as you apply the -1 to both sides, the equation will not change)

now,

6Y = -10

6Y = -10This means

Y= -5/3

Y= -5/3All you do now is plug this Y value back in to one of the original equationsX + (-5/3) =10

This means that X = 10 + 5/3 = 35/3

Y= -5/3All you do now is plug this Y value back in to one of the original equationsX + (-5/3) =10

This means that X = 10 + 5/3 =35/3

To show that these are the right answers, I’ll plug them back in to the equations

35/3 + (-5/3) = 30/3 =

10This one works.

35/3 - 5(-5/3) = 35/3 + 25/3 = 60/3 = 20This works because the first and second equation are satisfied. When added together, they equal 10. When subtracting the smaller variable (Y because -5/3 < 35/3) five times from the larger variable, the equation is satisfied.

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