Problem solving with linear and quadratic simultaneous equations

12 questions

1. Which equation is true for x = 2 and y = 5?
2. If I add together the pair of simultaneous equations 7x + 7y = 87 and 5x + 7y = 91, what is the resulting equation?
3. Multiply this equation by 5: 3x + 10 = 40
4. What is the value of x for equations 6x + 8y = 66 and x + 3y = 16?
5. What is the negative coordinate pair that solves both x^2 + y^2 = 40 and x - y = 4?
6. What is the negative coordinate pair that solves both x^2 + y^2 = 17 and x - y = 3?
7. 4 red and 5 blue boxes weigh 33g. 7 red and 2 blue weigh 24g. What is the mass of each box?
8. 7 red and 5 blue boxes weigh 86g. 5 red and 7 blue weigh 82g. What is the mass of each box?
9. 3 small & 5 large toys cost £185. 5 small & 3 large cost £175. What is the cost of each toy?
10. Using 4 hours of light A and 6 hours of light B consumes 240 watts. If 6 hours of A and 4 hours of B are used instead, it consumes 280 watts. What is the power consumption per hour for each light?
11. A publisher prints novels and textbooks. Printing 4 novels and 6 textbooks costs £320. Printing 6 novels and 4 textbooks costs £280. What is the printing cost for each type of book?
12. A café blends 3 kg of Brazilian beans (B) with 2 kg Columbian (C) to create a blend for £50. Another blend mixes 2 kg from B with 3 kg from C for £60. What is each bean price per kg?

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