Using linear equation formula we convert the given situation into mathematical statements illustrating the relationship between the unknowns (variables) from the information provided. Linear Equationis the equation of a straight 'line' and is also known as equations of the first order. What is the use of linear equations in real life? Linear equations are popular in science and in many everyday applications. Algebra could be used to solve real-life problems. Let us understand the linear equation formula in detail in the following sections.
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The standard form of a linear equation in one variable is represented as ax + b = 0, where, x is a variable, and a and b are the constants. While the standard form of a linear equation in two variables represented as ax + by = c, where, x and y are variables, and a, b and c are constants. Linear equation formula is given by:
y = mx + c
x and y are two variables,
c is a constant and,
m is the slope of the equation
Let us understand the linear equation formula better using the solved examples.
Solved Examples Using Linear Equation Formula
Example1: Jake's piggy bank has11 coins (only quarters or dimes) that have a value of S1.85. How many dimes and quarters does the piggy bank has?
Let us assume that:
Number of dimes = x
Number of quarters = y
Since there are 11 coins in total, x + y = 11 ⇒ y = 11 - x → (1)
The total value of the money in the piggy bank is $1.85 (185 cents). So we get the equation:
10x + 25y = 185
10x + 25(11 − x) = 185 (From (1))
10x + 275 − 25x = 185
−15x + 275 = 185
−15x = −90
x = 6
Substitute this in (1): y = 11 - 6 = 5
Answer: The number of dimes = 6; The number of quarters = 5
Example 2:John plugs in y = -3 in the equation 3x + 4y = 15. Find the value of x using the linear equation formula.