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# Linear Equations

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An introduction to

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### Linear Equations

1. 1. Practice Problem #1<br />Jennifer has a summer job cleaning swimming pools. After 30 minutes, a 5-foot-deep pool is filled to the 2-foot level. At the same rate, how long will it take to fill the pool entirely? <br />
2. 2. Practice problem #2<br />Simplify:<br />42t + 3p - -y + 16t – 3p/8 + y^2 + 45 <br />
3. 3. Linear equations and inequalities<br />Solving equations with the unknown variables on both sides<br />
4. 4. Example<br />Spencer is spending money, while his sister Sabina is saving it. At present, Spencer has \$100, but he spends about \$2 more than his allowance each week. Sabina has \$50, but she is saving about \$3 of her allowance each week. <br />Spencer: <br />Sabina: <br />
5. 5. AX + b = CX + D<br />SOLVING…<br />
6. 6. At what point does Spencer and Sabrina have the same amount? <br />Example #1 <br />A = 100 2w<br />A = 50 + 3w<br />100 – 2w = 50 + 3w<br />
7. 7. Same Place, Same time<br />Example #2<br />Kirbyand Claytonare skating the same direction along the shore of a frozen lake. Clayton is skating at a speed 4ft per second and is 12ft beyond the warming house. Kirby is skating at 13ft per second and is 30ft beyond the warming house…<br />
8. 8. At what time were the two in the same location??<br />
9. 9. SOlve<br />Example # 3<br />y= 391 – 16y<br />
10. 10. SOLve<br />Example # 4<br />2x – 5/3 = x + 1/6<br />