Begin with a verbal model to write the system of linear equations, then graph each equation. Which point is the solution to the system?
26 math problems, 16 science problems, see solution.
Practice makes perfect
We want to find how many problems in each subject we have for homework. Let's begin by using a verbal model to write a system of linear equations. We will use x to represent the number of math problems and y to represent the number of science problems. From the exercise, we know that we have a total of 42 math and science problems for homework.
x+ y= 42
We also know that we have 10 more math problems than science problems. Let's write this as an equation.
x= y+ 10
Now we can graph each equation in the system and look for a point of intersection, which will be the solution to the system of equations.
The graphs seem to intersect at the point (26,16). Finally, let's check if this point is a solution to the system of equations we created. We can check by substituting 26 for x and 16 for y in each equation and checking if the equations produce true statements.
