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Question: What are the values of \(x\) and \(y\) if \(2y + x = - 4\) and \(y - x = - 5\)?...

What are the values of xx and yy if 2y+x=−42y + x = - 4 and y−x=−5y - x = - 5?

Explanation

Solution

There are two variables xxand yygiven in the problem. Short out the two variables as a one variable by using the arithmetical operations. Find the one variable value and substitute the value in another equation. In this method easily we got the values of the variables.

Complete step-by-step solution:
There are two equations given to us. Let we use as a equation
2y+x=−42y + x = - 4…………………………………(1)\left( 1 \right)
y−x=−5y - x = - 5……………………..…………….(2)\left( 2 \right)
Now solve the equation (2)\left( 2 \right),we have,
y−x=−5y - x = - 5
We have to find one variable. so change the x variable to the right hand side, we get,
y=−5+xy = - 5 + x
Arrange the equations like variables to constant from higher derivatives, we get the equation,
y=x−5y = x - 5
Now we get the value of, y=x−5y = x - 5………………..…………………(3)\left( 3 \right)
Now substitute the value of yy in equation (1)\left( 1 \right),we get,
2y+x=−42y + x = - 4
Substitute the value of yy,we get,
2(x−5)+x=−42\left( {x - 5} \right) + x = - 4
Multiple the values inside the bracket,
2x−10+x=−42x - 10 + x = - 4
Now collect the variables at left hand side (LHS) and constants at the right hand side(RHS).we get ,
2x+x=−4+102x + x = - 4 + 10
Solving the above equation we get,
3x=63x = 6
Now we want to find the value of variable xx,so put the variable stable as left hand side, and the multiple term 33becomes a divisor of right hand side, now solve the equation, we get,
x=63x = \dfrac{6}{3}
x=2x = 2 ………………………………….(4)\left( 4 \right)
Here we find the value of xx variable.
Substitute this equation in equation (2)\left( 2 \right),we have,
y−x=−5y - x = - 5
Put x=2x = 2 we get,
y−2=−5y - 2 = - 5
Solve the equation,
y=−5+2y = - 5 + 2
y=−3y = - 3
Therefore the values of the variables are,
x=2x = 2;
y=−3y = - 3;

Note: This is an easy method to find the values of variables. But we must be careful in the places plus and minus symbols. First of all plan to find any one of the variables' values. Using the value find the other variables value. When the question is a little difficult you will use the cancellation method or cross multiplication method.