Maggie's brother is 3 years younger than twice her age the sum of their ages is 24. how old is maggie?

For this case, the first thing we must do is define variables.

We have then:

x: Maggie's age

y: Age of Maggie's brother

We write the system of equations that models the problem.

We have then:

We solve the system of equations.

For this, we use substitution:

From here, we clear the value of x:

Maggie is 9 years old

Maggie's age is 9

One variable linear equation is an equation that has a variable and the exponent number is one.

Can be stated in the form:

or

ax + b = c,

where a, b, and c are constants, x is a variable

Whereas the two-variable linear equation is a linear equation that has 2 variables and the exponent is one

Can be stated in the form:

x, y = variable

Let Maggie's age = x

Maggie's brother = y,

In the statement of the task:

we translate this sentence into the equation

y = 2x-3 ... equation 1

we translate this sentence into the equation

x + y = 24 ...equation 2

Both of these equations are equations that have 2 variables, so the solution can be used in 3 ways:

the solution is the intersection point of the two equations / lines.

the solution is we change one variable  into another variable form of an equation, then substitutes that variable in another equation

the solution is to eliminate one variable from the equation system.

to determine the variable x we eliminate the variable y first , or vice versa.

We use the second method: substitution

we substitute equation 1 into equation 2 :

So Maggie's age:

each of their ages

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Three times b less than 100

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6 = 4x + 9y solve for y

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Keywords: variable, equation, substitution, elimination, graph, Maggie's age

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus