Write and Solve a System of Equations Refer to the application at the beginning of the lesson. Write and solve of equations to determine how many seats are in each section of the amphitheater. CONCERTS a system : seats in section A = seats in section B z = lawn seats ir Understand Define the variables. / eReal-World Career Plan There are 19,200 seats. x+V+z:79,200 Music Management Music management involves acting as the talent manager to the arlists. Other duties include negotiating with record labels, music promoters, and tour promoters. Managers The total revenue is $456,000. Equation t 30x+25y*202:456,000 Equation 2 There are twice as many seats in section B as in section A. A Solve usually earn a percentage :2x Solve the system. Step of the artist's income. Equation 3 t Substitute a :2x in the first two equations. x+y+z=79,200 A bachelor's degree Equation I xl2x*z:79,200 is usually required. Y:Dt 3x+z=L9,200 Add. + 25y t 20z = 456,000 Equation 2 30x 30x + 25(2x) 80x Step 2 Solve the system of two equations in two variables. 3x + z look for a Pattern +ZOz:456,000 y:2sr + 202:456,000 Simplify. 80x + = t9,200 IIiilElFFil ' 202:456,000 2oz = _a84,000 (+) 80x + 202:456,000 _-60x 20x Looking for a pattern can help to identify a :72,000 r : 3600 function and write an equation. Step I Substitute to find z. 3x + z :79,200 3(3600) 10,800 Step 4 * * z z :79,200 :79,200 z :8400 ,: : *I --!--.- 1600 Distribute. Simplifu. Substitute to find y. ,,U-LA _ 4.. : Remaining equation in two variables x: ZpeOOl Equation 3 or 7200 x = 3600 The solution is (3600, 7200, 8400). There are 3600 seats in section A, 7200 in section B, and 8400 lawn seats. Check Substitute the values into either of the first two equations. Guided Practice j 5. Ms. Garza invested $50,000 in three different , , , accounts. She invested three times as much money in an account that paid 8% interest than an u..orrlt that paid 107o interest. The third account earned 12% interest. If she earned a total of $5160 in interest in a year, how much did she invest in each account? b 17O Chapter 3 Systems of Equations and lnequalities Personal Tutor slencoe.com

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