•Solve the following by: • y = 2x Show y=x+3 all your •1.) Graphing Work •2.) Substitution •3.) Linear Combination (+)
Bellwork
Today’s Objective
•To be able to write a linear system word problem and solve it.
Example #1
•Read example 2 on page 368 and find the two items that were sold in the problem and the total sold. •Style A shoes •Style B shoes
Example #1
•Let Style A = x •Let Style B = y •Total sold = 240 So…. •x + y = 240 (1st Equation)
Example #1
• Receipts for Style A = 66.95x • Receipts for Style B = 84.95y
•Total Receipts = 17,652 So…. •66.95x + 84.95y = 17,652 (2nd Equation)
Solve by Substitution
•x + y = 240 •66.95x + 84.95y = 17,652
•x + y = 240 (Solve for x) •x + y - y = 240 - y •x = 240 - y
Solve by Substitution
•x = 240 - y •66.95x + 84.95y = 17,652
•66.95(240-y) + 84.95y = 17652
Solve by Substitution
• 66.95(240-y) + 84.95y = 17652 • 16068 - 66.95y + 84.95y = 17652 • 16068 + 18y = 17652 (subtract 16068)
•18y = 1584 (divide by 18) • y = 88 •Now Find x
Solve by Substitution
•Since y = 88 and •x = 240 - y then •x = 240 - 88 •x = 152 •Style A = 152, Style B = 88
Steps •#1 ~ Make a list and pick the variables •#2 ~ Write the equations •#3 ~ Solve
Example #2
•Step #1 •Let Total Sales = x •Let Total Earnings = y •Step #2 •y = 20,000 + .01x (1st job) •y = 15,000 + .02x (2nd job)
Solve by (L.C. add)
•y = 20,000 + .01x •y = 15,000 + .02x •y = 20,000 + .01x (times by -1) •-y = -20000 - .01x •y = 15000 + .02x (add)
• You Finish to find x
•y = 20,000 + .01x •y = 15,000 + .02x •y = 20,000 + .01x (times by -1) •-y = -20000 - .01x •y = 15000 + .02x (add) •0 = -5000 + .01x
Solve by (L.C. add)
Solve by (L.C. add)
•0 = -5000 + .01x •0+5000=-5000+5000+.01x •5000 = .01x (divide by .01) •500,000 = x
• You must sell $500,000 in supplies for both jobs to be equal in salary.
Solve by (L.C. add)
• What salary would you earn? • Since y = 20,000 + .01x & • x = 500,000 then
•y = 20,000 +.01(500000) •y = 20,000 + 5,000 •y = 25,000