types of solution of system of linear equation

A system of linear equations consists of two or more linear equations made up of two or more variables such that all equations in the system are considered simultaneously. In order to investigate situations such as that of the skateboard manufacturer, we need to recognize that we are dealing with more than one variable and likely more than one equation. How can the company determine if it is making a profit with its new line? How many skateboards must be produced and sold before a profit is possible? In this section, we will consider linear equations with two variables to answer these and similar questions. The manufacturer tracks its costs, which is the amount it spends to produce the boards, and its revenue, which is the amount it earns through sales of its boards. Solve the following linear equations & identify whether the given linear equations have one, zero or infinite solutions.A skateboard manufacturer introduces a new line of boards. We have 144 = 144, which is a True statement & it will be true for any value of the variable x.įrom the above examples we can say that, the linear equation will have infinite solutions if it is satisfied by any value of the variable or every value of the variable makes the given equation a true statement.

Hence the given linear equation has Infinite solutions or the number of solutions is infinite.Įxample 2: Consider the equation 15 ( x + 9) = 24 x + 9 – (9 x – 126) We have -35 = -35, which is a True statement & it will be true for any value of the variable x. Subtracting 25 x from both sides, 25 x – 25 x – 35 = 25 x – 25 x – 35

Hence, the given linear equation has no solution or the number of solutions is zero.įrom the above examples, we can see that the variable x disappears / gets eliminated & hence we say that the linear equation will have Zero or no solution if it can’t be satisfied by any value of the variable or there does not exist any value of the variable which makes the given equation a true statement.Įxample 1: Consider the equation 25 x – 35 = 5 (5 x + 4) – 55. We have 27 = 9, which is a false statement since it can’t be true for any value of the variable x. Subtracting 24 x form both sides, 24 x – 24 x + 27 = 24 x – 24 x + 9.

Hence, the given linear equation has zero solution or the number of solutions is zero.Įxample 2: Consider the equation 3( x + 9) + 21 x = 24 x + 9. We have -35 = -27 which is a false statement since it can’t be true for any value of the variable x. Example 1:Consider the equation 7 x – 35 = 5 x + 2 x – 27.

Types of solution of system of linear equation