If you add Natalie's age and Fred's age, the result is 40. If you add Fred's age to 4 timesNatalie's age, the result is 76. Write and solve a system of equations to find how old Fred and Natalie are.

Natalie is 12 years and Fred is 28 years

Step-by-step explanation:

lets assume Natalie's age is X and Fred's age is Y

From the first sentence: X+Y = 40

From the second sentence: Y + 4X = 76

lets rearrange the equations

X+Y =40 equation 1

4X+Y=76 equation 2

To solve both equations, we will have to look for a way to eliminate one of the unknown to leave us with one unknown. since there are two +Y in both equations, we can subtract both equations to eliminate Y. Please note that whatever you do to one of the unknown in this equations applies to all other numbers & alphabets

So: 1. X - 4X = -3X

2. Y - Y = 0

3. 40 -76 = -36

writing the equation as one will be -3X = -36

X = 12

Put X = 12 into any of the equation

By putting X as 12 into equation 1 : 12 + Y = 40

Y = 40 -12 =28

Recall that Natalie is X and Fred is Y

Therefore Natalie is 12 years and Fred is 28 years

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To crosscheck put in the gotten answers into the equations

X+Y =40 12 + 28 = 40

4X+Y=76 4(12) + 28 = 76