Question

How do you solve for \[z\] in \[xz+y=1+z\] ?

Answer 1

Hint:This is a linear equation in three variables as there are three variables in an equation i.e. \[x,y,\ and\ z\]. In the given question, we have been asked to solve the equation for \[z\], to solve this question we need to get ‘\[z\]’ on one side of the “equals” sign, and all the other numbers and variables on the other side. To solve this equation for a given variable ‘\[z\]’, we have to undo the mathematical operations such as addition, subtraction, multiplication and division that have been done to the variables.

Complete step by step answer:
We have the given equation:
\[xz+y=1+z\]
Subtract \[y\]from both the sides of the equation, we get
\[xz+y-y=1+z-y\]
Simplify the above equation, we get
\[xz=1+z-y\]
Subtract \[z\]from both the sides of the equation, we get
\[xz-z=1+z-y-z\]
Simplify the above equation, we get
\[xz-z=1-y\]
Taking \[z\]as common from the left-hand hide of the equation, we get
\[z\left( x-1 \right)=1-y\]
Transposing \[\left( 1-x \right)\] to the right-hand side of the equation, we get
\[\therefore z=\dfrac{1-y}{x-1}\]

Therefore, \[z=\dfrac{1-y}{x-1}\] is the required solution.

Note:The important thing to recollect about any equation is that the ‘equals’ sign represents a balance. What the sign says is that what’s on the left-hand side is strictly an equal to what’s on the right-hand side. It is the type of question where only mathematical operations such as addition, subtraction, multiplication and division is used.In the given question, no mathematical formula is being used; only the mathematical operations such as addition, subtraction, multiplication and division are used.
-Use addition or subtraction properties of equality to gather variable terms on one side of the equation and constant on the other side of the equation.
-Use the multiplication or division properties of equality to form the coefficient of the variable term equivalent to 1.