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Module 5 Chapter Review Systems of Equations and Linear Inequalities
** You may have to solve these on a separate sheet of paper. Remember that we will be reviewing this in class tomorrow! Be sure to check my weebly page tonight for extra practice and video reviews. Solve the following Systems of Linear Equations 3𝑥 + 4𝑦 = 23 5𝑥 + 3𝑦 = 31 2𝑥 + 3𝑦 = 14 4𝑥 + 6𝑦 = 28 3𝑥 + 2𝑦 = 20 9𝑥 + 6𝑦 = 38 4𝑥 + 2𝑦 = 8 5𝑥 + 3𝑦 = 9 3𝑥 − 4𝑦 = 13 𝑦 = −3𝑥 − 7
Constance owns a small lunch cart. She changes her menu daily. Yesterday, she offered a chef salad for $5.75 or a hoagie for $5.00. She sold 85 lunches for a total of $464. Determine how many chef salads and hoagies she sold. For each of the systems of inequalities, determine if the given coordinates are solutions to the system. 𝑦 ≤ 3𝑥 − 5 𝑦 ≥ 𝑥 + 2 a. ( 6 , 10 ) b. ( 1 , 4 ) c. ( 8 , 15 ) 𝑦 > −2𝑥 + 9 𝑦 ≥ 5𝑥 − 6 a. ( -‐2 , -‐5 ) b. ( -‐1 , 12 ) c. ( 5 , 0 )
𝑦 < −12 𝑥 + 9
𝑦 > 6𝑥 − 10 a. ( -‐2 , -‐5 ) b. ( 7 , 3 ) c. ( -‐8 , 10 ) Graph the following inequalities. Justify the region you shade by showing three points in the region as being solutions to the problem. Show a point you have tested to prove your shaded region is accurate. 3x− 4y ≥ 12 𝒙+ 𝟔𝒚 < 𝟔
Graph each set of inequalities and determine the solution region. 𝑥 − 𝑦 < −6 −2𝑦 ≥ 3𝑥 − 18 5𝑥 + 2𝑦 ≥ −10 3𝑥 − 2𝑦 ≤ 18 3𝑥 − 9𝑦 ≥ 27 Solve the following compound inequalities. −4 ≤ −3𝑥 + 1 ≤ 12 2𝑥 + 7 < 10 𝑜𝑟 − 2𝑥 + 7 > 10 Convert the following to slope-‐intercept form ( y = mx + b) 3𝑥 + 6𝑦 = −48 3𝑥 + .5𝑦 = 1.5 Convert the following to standard form (ax + by = c…. if you get fractions you must multiply out for whole numbers)
y = 14 x+ 6
𝑦 = 3𝑥 + 4 How many solutions might a linear equation have? How many solutions might a linear inequality have? How many solutions might a systems of equations have? How many solutions might a system of inequalities have?
Write the system of inequalities whose solution set is shown below