Lucy had math and reading homework tonight. Lucy can solve each math problem in 5 minutes and she can read each page in 2.5 minutes. The number of math problems Lucy solved is 3 times the number of pages she read and it took her 105 minutes to complete all of her homework. Graphically solve a system of equations in order to determine the number of math problems Lucy solved,x, and the number of pages she read, y.

Answer:[tex]x=18,y=6[/tex],  graph is there for reference.Step-by-step explanation:Given,[tex]x[/tex] is the number of math problem Lucy solved.[tex]y[/tex] is the number of  pages she read.She can do each math problem in  [tex]5[/tex] minutes, therefore she can solve [tex]x[/tex] number of questions into [tex]5 \times x=5x[/tex] minutes.She can read each page in [tex]2.5[/tex] minutes, therefore she can read [tex]y[/tex] pages in 2.5y minutes.As per given detail,[tex]5x+2.5y=105[/tex] equation 1.And,It is given that number of math problems Lucy solved is 3 times the number of pages she read.[tex]x=3y[/tex] equation 2.We need to find [tex]x[/tex] and [tex]y[/tex] intercept of each of the equation to graph them.For [tex]x-intercept[/tex] put y=0We will get [tex]x=\frac{105}{5} =21[/tex]Thus the point is [tex](21,0)[/tex]Let us find [tex]y-intercept[/tex] by assuming [tex]x=0[/tex]we get [tex]y=\frac{105}{2.5} =42[/tex]Thus the point is [tex](42,0)[/tex]Join these two points.Similarly considering the other equation [tex]x=3y[/tex]Here x-intercept would be at [tex]y=0[/tex] We will get [tex]x=0[/tex]Thus the point is [tex](0,0)[/tex]Let us assume on more point, say [tex]x=30[/tex] , we get [tex]y=10[/tex]Thus the point is [tex](30,10)[/tex]Join these two points.We will get a point of intersection at [tex](18,6)[/tex]Thus [tex]x=18[/tex] and [tex]y=6[/tex]