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CP Algebra Name: System of Equations Study Guide Rewrite the following equations in slope-­‐intercept form (y = mx + b) and solve the system on the graphing calculator. x + y = 13
y = 3x
1. 2. x −y =5
x + 2y = 21
REWRITE REWRITE €
y = 3x
y = −x +13
1
21 y = x −5
y =− x+
2
2
ANSWER ANSWER (9, 4) (3, 9) €
2x + 6y = 18
3x + 5y = 7
3. 4. 3x + 2y = 13
2x − 3y = 11
REWRITE REWRITE €
1
3
7
y =− x+3
y =− x+
3
5
5
3
13
2
11
y =− x+
y= x−
2
2
3
3
ANSWER ANSWER (3, 2) (4, -­‐1) €
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Solve the following application problems using system of equations. Use either substitution or elimination to solve the problem. You must show your work and write an appropriate answer to the question. 5. 20,000 tickets were sold to the One Republic concert. Stage level seats cost $105 and higher level seats cost $75. If the total money collected from selling tickets was $1,740,000, how many tickets of each type were sold? VARIABLES S – stage level seats [$105 per seat] H – higher level seats [$75 per seat] EQUATIONS S + H = 2,000
105S + 75H = 1,740,000
ANSWER 8,000 stage level seats [S = 8,000] 12,000 higher level seats [H = 12,000] 6. Brodie’s Gourmet Pretzel Shop specializes in selling the very finest chocolate covered pretzels. Banks bought 4 white chocolate pretzels and 6 dark chocolate pretzels for $10.50. Holden bought 8 white chocolate and 3 dark chocolate pretzels for $9.75. What was the cost of each type of pretzels. VARIABLES W – white chocolate pretzels D – dark chocolate pretzels EQUATIONS 4W + 6D = $10.75 8W + 3D = $9.75 ANSWERS $1.25 for dark chocolate pretzels [D = 1.25] $0.75 for white chocolate pretzels [W = 0.75] 7. Tyler is catering a banquet for 250 people. Each person will be served either a chicken dish that costs $5 each or a beef dish that cost $7 each. Tyler spent $1500. How many dishes of each type did Tyler serve? VARIABLES C – Chicken dish [$5 per dish] B – Beef dish [$7 per dish] EQUATIONS C + B = 250 5C + 7B = 1,500 ANSWER 125 Chicken dishes [C = 125] 125 Beef dishes [B = 125] 8. The math club and the science club had fundraisers to buy supplies for a hospice. The math club spent $135 buying six cases of juice and one case of water. The science club spent $110 buying four cases of juice and two cases of bottled water. How much did a case of juice cost? How much did a case of bottled water cost? VARIABLES J – cases of juice W – cases of water EQUATIONS 6J + 1W = 135 4J + 2W = 110 ANSWER 20 cases of juice [J = 20] 15 cases of water [W = 15]