We want to find how many nurses and doctors a hospital employs by writing and solving a system of linear equations using the Substitution Method. We will do these things one at a time, starting with forming the system. Let's use x to represent the number of nurses and y to represent the number of doctors.
Number of nurses: & x Number of doctors: & y
From the exercise, we know that the hospital employs a total of 77 nurses and doctors. Let's write this as an equation.
x+ y= 77
We also know that the ratio of nurses to doctors in the hospital is 9:2. We can write this as 92= y x. Let's rewrite this equality so it will be easier for us to create a system of equations.
9/2=y/x ⇔ y=9 x/2
With two equations created, we can combine them into a system of equations. Let's take a look.
x+y=77 & (I) y= 9x2 & (II)
Now we are ready to solve this system to find the numbers of nurses and doctors that the hospital employs. First, notice that Equation (II) is already solved for y. Let's substitute 9x2 for y in Equation (I) and solve it for x.
Now that we have a value for x, we can substitute its value into either equation for x and solve for y. Let's substitute 14 for x in Equation (I) for simplicity.
