## Solve: ` 1/(a+b+x) = 1/a + 1/b + 1/x`

We’ve seen how to write a system of equations with an augmented matrix, then how to get row-echelon form using row operations and back-substitution. Now we’ll use row-echelon form to solve a three-by-three system of linear equations. The general concept is to use row operations to delete all but one variable, then back-substitute to solve for the remaining variables.
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This is a contingent structure with an infinite number of solutions, as shown by the identity [latex]0=0[/latex]. Then we look for a generic solution. We can solve for [latex]z[/latex] in terms of [latex]x[/latex] by solving the second equation for [latex]y[/latex] and substituting it into the first equation.

## If x+1/x=3 then find the value of x^3+1/x^3. if x+1/x=6 find x2+1

We’ve only solved equations with one unknown variable so far. Two equations are required to solve for two unknown variables, and these equations are known as simultaneous equations. The values of the unknown variables that satisfy both equations at the same time are called solutions. Where there are (n) unknown variables, (n) independent equations are required to find a value for and of the (n) variables.
For two unknown variables, we must solve two independent equations. Simultaneous equations can be solved algebraically using substitution and elimination techniques. We’ll also illustrate how to solve a system of simultaneous equations graphically.
This section can be combined with the chapter on functions and graphs with graphs of linear equations in the chapter on functions and graphs. It’s likely that you’ll need to go over plotting graphs of linear equations with your students before starting this section.
It’s also crucial that learners are given graphs or encouraged to draw accurate graphs on graph paper to assist them in graphically solving simultaneous equations. In this section, graph sketching software can be used to ensure that graphs are correct.

### Marginal revenue, average cost, profit, price & demand

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Once upon a time, in the city of Chongqing, there lived a very wealthy man who lost all of his possessions and jewels and became very poor. He was so poor that he could only make a living by working 24 hours a day, seven days a week. He went to bed late one night and slept soundly. He was tired, dejected, and sick to his stomach. He dozed off and dreamed that a wise old soul appeared to him and told him, “Your fortune is in Beijing; go there and search it.”
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### Check whether the value given in the brackets is a solution to

There are 150 orange trees in Mr. Madhusudan’s orange garden. There are 5 more trees in each row than there are in each column. Using the flow chart below, calculate the number of trees in each row and column.
Mr. Kasam owns and operates an earthenware potter’s shop. On a regular basis, he makes a certain number of pots. Each pot costs Rs 40 to make, which is more than 10 times the total amount of pots he makes in a day. Find the production cost of one pot and the amount of pots he makes per day if the total cost of all pots per day is Rs 600.
The trapezium AB || CD in the adjacent figure has a surface area of 33 cm2. Find the lengths of both sides of the ABCD using the details in the diagram. To find the answer, fill in the blanks.
Mr. Dinesh owns a farm in the village of Talvel. The farm’s length is ten meters longer than its width. He dug a square-shaped pond within the farm to collect rainwater. The width of the farm is 13 times the length of the pond. The farm covers an area 20 times that of the pond. Determine the farm’s length and width, as well as the size of the pond.