# Problem Solving Using Linear Equations

In this case both equations have "y" so let's try subtracting the whole second equation from the first: So now we know the lines cross at x=1. The problem should list the Y- intercept, a starting amount of something and a slope, or a rate of change.Now, 4 years ago the ratio between A’s age and B’s age 4 years hence is 1:1. But we need to calculate the ratio between A and B such that (5x 4) :(3x – 4) I hope, your concept would have been cleared and you now evolve better understanding about it and will be able to solve questions on your own.

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Write one of the equations so it is in the style "variable = ...": We can subtract x from both sides of x y = 8 to get y = 8 − x. Write one of the equations so it is in the style "variable = ...": Let's choose the last equation and the variable z: First, eliminate x from 2nd and 3rd equation.

Well, we can see where they cross, so it is already solved graphically. Let's use the second equation and the variable "y" (it looks the simplest equation). Now repeat the process, but just for the last 2 equations.

Solution: Let the age of daughter be x and that of mother will be y. x 12, mother’s age after twelve years would be (y 12) and also it will be twice of her daughter, y 12 = 2(x 12). You’ll find three people here and you must be worried how to solve equations of 3 variables. And it’s Cleary stated that the age of Sneh is 1/6 of his father. Now assume Vimal’s age be z, so after 10 years Vimal age would be z 10 and Sneh’s father age will be twice of Vimal. Also, currently her daughter’s age is 1/6The final equations are x = 9/7* (x – 8) y = x/6 Solving the first equation, we get age of Farah = 36 years. 2x 4 and 5x 4 the ratio between their ages become Case 1: Whole number form Numerical: The sum of present ages of father and son is 8 years more than the present age of the mother. Since, the sum of the present ages of father and son is 8 years more than the mother i.e. After 8 years, their ages will be 32 and 28 and hence, the ratio would be i.e.

And the first line clearly states that at present the age of mother is thrice of daughter. Hence her daughter’s present age is 6 years but we need her age 3 years back. Solution: It’s given in question that the current age of Amit and his father are in ratio 2:5. 8:7 Case 3: Combination of age after k years and before k years.

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We can make two equations (d=distance in km, t=time in minutes) The two equations are shown on this graph: Our task is to find where the two lines cross. Let's use the first one (you can try the second one yourself): We can start with any equation and any variable.

And we can find the matching value of y using either of the two original equations (because we know they have the same value at x=1).

Now, Problem on ages can be categorized into three types, i.e.

Questions based on calculating the present age, Questions to determine the age of person after k years and questions that calculate age of a person before k years.

## Comments Problem Solving Using Linear Equations

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