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The sum of two numbers is 30 and their difference is 2.  Find the two numbers by writing and solving a
system of equations

Sagot :

The numbers are 14 & 16.

The equations you need to solve are:

x + y = 30
x - y = 2  ==>  (redefine in terms of y)  y = x - 2

substitute into first equation

x + x - 2 = 30
2x = 30 + 2
x = 32/2 = 16

16 + y = 30
30 - 16 = y = 14

x = 16
y = 14

And that's how that is done.

The correct answer is:

The numbers are 14 and 16.

Explanation:

Let x and y represent the numbers. Since the sum of the numbers is 30, this gives us the equation

x+y = 30.

Since the difference of the numbers is 2, this gives us the equation

x-y = 2.

This gives us the system

[tex] \left \{ {{x+y=30} \atop {x-y=2}} \right. [/tex]

To solve this, we will eliminate one variable. Since the coefficients are all the same, but the y-variables have different signs, we will eliminate them by adding the equations together:

[tex] \left \{ {{x+y=30} \atop {+(x-y=2)}} \right.
\\
\\2x=32 [/tex]

Divide both sides by 2:

2x/2 = 32/2

x = 16.

Substitute this back into our first equation:

16+y=30

Subtract 16 from each side:

16+y-16=30-16

y=14

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