Question

What is the first step that is necessary to solve this system?



The Rams scored 100 points against the Indians making 42 combined two- and three-point shots. The following system displays the points made by the Rams.



3x + 2y = 100

x + y = 42

Answer 1

To solve the system of equations given:

3x + 2y = 100 (1)
x + y = 42 (2)

where x represents the number of three-point shots and y represents the number of two-point shots, it is often easiest to start with the equation that is simpler to manipulate. In this case, equation (2) is simpler because its coefficients are smaller and the equation is already in a form such that one variable can be easily expressed in terms of the other.

Let's solve equation (2) for one of the variables, then substitute it into equation (1). For example, we can solve for y in terms of x from equation (2):

y = 42 - x (3)

Now we plug equation (3) into equation (1) to get an equation with one variable:

3x + 2(42 - x) = 100

Simplify and solve for x:

3x + 84 - 2x = 100
x = 100 - 84
x = 16

Use the value of x to find y by substituting it back into equation (3):

y = 42 - 16
y = 26

So, the solution to the system is x = 16 and y = 26, meaning the Rams made 16 three-point shots and 26 two-point shots to score a total of 100 points with 42 combined shots.