if a=[2/6 4/5] and b= [y/6 x/5] then find the values of x and y
Answers
Step-by-step explanation:
I'm not sure why I have been given a request to answer this question given there are 100+ answers for this already.
What you have here are two equations:
x+y=5x+y=5 [1]
xy=6xy=6 [2]
To solve for xx and yy, you should rearrange one of the equations for one of the variables xx or yy. Choose equation [1] to rearrange for yy, because it is easy to do so.
y=5−xy=5−x [3]
Now, substitute this expression into equation [2]:
x(5−x)=6x(5−x)=6
Now use this equation to solve for xx. Firstly expand the parentheses:
5x−x2=65x−x2=6
Rearrange the terms so that they are all on one side of the equation:
x2−5x+6=0x2−5x+6=0
What you have here is a quadratic equation. There are many ways to solve a quadratic equation but I will choose the easiest method for this problem.
Factorise the quadratic expression on the left-hand side of the equation by using the product-sum method (or by decomposition):
(x−2)(x−3)=0(x−2)(x−3)=0
The null factor law gives x=2x=2 or x=3x=3 as the solution.
Now, substitute x=2x=2 or x=3x=3 into equation [3] to get the value of y:
when x=2x=2, then y=5−2=3y=5−2=3
when x=3x=3, then y=5−3=2y=5−3=2
Therefore, there are two solutions to these simultaneous equations, which are: (2,3)(2,3) and (