Question

How do you solve a word problem with $3$ variables?

Answer 1

Steps for Solving a Word Problem with $3$ variables Using a Linear Equation:

Step 1: Write a system of linear equations that represents the situation given in the question using 3 variables.

for example, $x+y=0$ …..(1)

$y+1=0$ ……(2)

$z+x-y=2$ …….(3)

Step 2: Use substitution method to find the first variable.

$y+1=0$

$\Rightarrow$ $\mathit{y}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{1}$

Step 3: Substitute the first variable from Step 2 into an equation that relates to a second variable and solve for that variable.

Substitute the value of $y$ in equation (1), we get

$x-1=0$

$\Rightarrow$ $\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}$

Step 4: Substitute the values found from Step 2 and Step 3 into the equation with all three variables and solve for the remaining variable.

Finally substitute the value of $x$ and $y$ in equation (3), we get

$z+1-(-1)=2$

$\Rightarrow$ $z+1+1=2$

$\Rightarrow$ $z+2=2$

$\Rightarrow$ $\mathit{z}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}$

Hence, we can solve a word problem with three variables by following these steps.