IB Al- B NAHEL PARENT 133 C : Systems of Equations: Chapter Test 2 D: 1. What is the solution to the following system of equations? 9x + 5y = 125 Br + 6y = 136 a. (5, 16) b. (16, 5) c (12, 7) d. (7. 12) 2. A grade ten class has a total of 33 students. If there are 3 less boys than girls in the class, which system of equations below represents this situation? * represents the number of boys y represents the number of girls a. 33-x=y b. x+y= 33 C 33+1=y d. 33-x =3+y y - 3 -x y+3=x x = 33y y -3=3x 3. What value must be assigned to "m" for this system of equations to have an infinite number of solutions? y =-2r+10 y+2x = m a. 2 b. -10 C 10 d. -2 4. A system of equations is graphed on the My Calculations Cartesian plane below. Solve this system of equations. 16- 154 14+ 13- 12 (8, 11) 10 97 (16, 9) (8, 7) (16, 7) 10 11 12 13 14 15 168. A school auditorium holds 400 people. The annual talent show is about to take place and My Calculations the school is selling either premium seats for $10 each or regular seats for $7 each. If the number of regular seats is 250 more than twice the number of premium seats, how much will the school earn in revenue if the auditorium is filled to capacity? 5 9. Jeff, Andy and Joe like to play darts. The following table shows the points received already in the yellow section and the amount of darts that landed in the other coloured sections of the dart board. colour player Black section Red section Yellow section Total points 7 darts 175 Jeff 3 darts 10 points 225 Andy 5 darts 8 darts 5 points Joe 15 points ? 4 darts 6 darts How many total points did Joe score? My Calculations5. Here are 3 linear systems of equations: c. 5y = 15x +20 b. 10y -20x = 60 a. y = 5x -10 3y =9x +12 2y - 4x =-16 2y - 2r =10 11 Indicate whether the systems above have one solution, no solution or an infinite number of solutions. 6. Tony is an enthusiastic gardener. He plants a My Calculations garden that produces exceptional tomatoes and cucumbers. This summer, he plans to plant a total of 54 plants and he has purchased twice as many tomato plants as cucumber plants. Next year Tony wants to triple the amount of vegetable plants in his garden while respecting the same ratio of tomatoes and cucumbers. How many tomato and cucumber plants will he purchase next year? 15 7. The grade 11 girls are trying to raise money My Calculations for their graduation dance. It has been a tradition to sell handmade bracelets and necklaces to raise funds. Two years ago the girls sold 23 bracelets and 19 necklaces for a profit of $179.25. Last year the girls sold 27 bracelets and 18 necklaces for a profit of $186.75. This year the girls have made 30 bracelets and 25 necklaces. How much money will the raise if the sell all their jewelry? 15