Karen spend 11 hrs doing babysitting and 7 hrs doing music lessons by solving the linear equation.
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
A linear equation is an algebraic equation in which each term has an exponent of 1, and which, when plotted on a graph, always yields a straight line. It is called a "linear equation" for this reason.
Both linear equations with one variable and those with two variables exist.
Ax + B = 0, where A and B are both real integers, and x is the only variable, is the standard form or general form of a linear equation in one variable. Ax + By = C is the formula used to describe linear equations with two variables, where x and y are the variables and A, B, and C are any real values.
Total number of hours babysitting and music lessons be x and y hrs respectivly.
Therefore x + y = 18 (i)
and, 5x + 12y = 139 (ii)
Multipling equation (i) with 5 then subtracting from (ii) we get,
5x + 12y - 5x - 5y = 139 - 90
⇒ 7y = 49
⇒ y = 7.
When y = 7 putting this value in equation (i) we get x = 11.
Karen spend 11 hrs doing babysitting and 7 hrs doing music lessons.
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