As we know that linear equations in two variables could be solved using substitution method or elimination method. Now let us learn some applications of simultaneous equations which occurs in our day to day life. we could describe the real situation problem in words, which we call as word problem. Let us solve the linear equations in two variables word problems by following the steps below:
Read the problem unless you understand and find the unknown quantities which we have to calculate. Name the quantities with a variable name like a,b,c, x, y, z...
Determine which variables has to be solved.
understanding the problem, formulate the equations according to the problem. If two variables has to be solved we need two simultaneous equation.
Let uis solve the linear equation in two variables word problem using substitution method or elimination method.
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Sol:
Let $x be the cost of one bush and $y be the cost of one tree.
So, 13x + 4y = 487
6x + 2y = 232
On solving these two equations, we get x = 23 and y = 47
Sol:
Let "l" be the length and"b" be the breadth of the rectangle.
Area = lb square units
area of a rectangle is reduced by 9 square units if its length is reduced by 5 units and the breadth is increased by 3 units
lb - 9 = (l-5)(b+3)
`=>`
area is increased by 67 square units, if we increase the length by 3 units and breadth by 2 units
lb + 67 = (l+3)(b+2)
2l + 3b - 61 = 0
On solving these two equations we get l = 17 units and b = 9 units.
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