Answer :

carlosego

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:

[tex] y = 2x-3

x + y = 24
[/tex]

We solve the system of equations.

For this, we use substitution:

[tex] x + (2x-3) = 24
[/tex]

From here, we clear the value of x:

[tex] 3x - 3 = 24

3x = 24 + 3

3x = 27
[/tex]

[tex] x = \frac{27}{3}

x = 9
[/tex]

Answer:

Maggie is 9 years old

ardni313

Maggie's age is 9

Further Explanation

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

Can be stated in the form:

[tex] \large {\boxed {\bold {ax=b}} [/tex]

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:

[tex] \large {\boxed {\bold {ax + bx = c}}} [/tex]

x, y = variable

Let Maggie's age = x

Maggie's brother = y,

In the statement of the task:

  • Maggie's brother is 3 years younger than twice her age

we translate this sentence into the equation

y = 2x-3 ... equation 1

  • The sum of their ages is 24

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:

  • 1. graph system

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

  • 2. substitution

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

  • 3. elimination

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 :

[tex]\displaystyle x+2x-3=24[/tex]

[tex]\displaystyle 3x-3=24[/tex]

[tex]\displaystyle 3x=27[/tex]

[tex]\displaystyle x=9[/tex]

So Maggie's age: [tex]\large{\boxed{\bold{9}}[/tex]

Learn more

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

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