Your teacher is giving you a test worth 100 points containing 40 problems. There are 2 point questions and 4 point questions on the test. How many of each type of question are on the test?

Answer:Number of 2-point questions = 30Number of 4-point questions = 10Step-by-step explanation:Let the number of 2 point questions = [tex]x[/tex]Let the number of 4 point questions = [tex]y[/tex]Sum equation:Total number of questions can be given by =[tex]x+y[/tex]Total number of questions = 40So, we have :[tex]x+y=40[/tex]Points equation:Total points for [tex]x[/tex] number of 2 point question = [tex]2x[/tex]Total points for [tex]y[/tex] number of 4 point question = [tex]4y[/tex]Total points in the test can be given by = [tex]2x+4y[/tex]Total points in the test = 100So, we have :[tex]2x+4y=100[/tex]So, the system of equations is:A) [tex]x+y=40[/tex]B)  [tex]2x+4y=100[/tex]Rearranging equation A, to solve for [tex]y[/tex] in terms of [tex]x[/tex] Subtracting both sides by [tex]x[/tex] [tex]x+y-x=40-x[/tex] [tex]y=40-x[/tex] Substituting value of [tex]y[/tex] we got from A into equation B. [tex]2x+4(40-x)=100[/tex] Using distribution. [tex]2x+160-4x=100[/tex] Simplifying. [tex]-2x+160=100[/tex] Subtracting both sides by 160. [tex]-2x+160-160=100-160[/tex] [tex]-2x=-60[/tex] Dividing both sides by -2. [tex]\frac{-2x}{-2}=\frac{-60}{-2}[/tex] [tex]x=30[/tex] We can plugin [tex]x=30[/tex] in the rearranged equation A to get value of [tex]y[/tex] [tex]y=40-30[/tex] ∴[tex]y=10[/tex] Thus, number of 2-point questions = 30Number of 4-point questions = 10