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:
\(\large {\boxed {\bold {ax=b}}\)
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:
\(\large {\boxed {\bold {ax + bx = c}}}\)
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:
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 :
\(\displaystyle x+2x-3=24\)
\(\displaystyle 3x-3=24\)
\(\displaystyle 3x=27\)
\(\displaystyle x=9\)
So Maggie's age: \(\large{\boxed{\bold{9}}\)
Learn more
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Keywords: variable, equation, substitution, elimination, graph, Maggie's age
