1.1 Integers and Rational Numbers

www.ck12.org Chapter 12. Systems of Linear Equations(0.6, 0.15 and 0.05). The two pieces of critical information are the final volume (500 ml) and the final amount ofsolute (15% of 500 ml = 75 ml). Our equations will look like this:Volume equation: x + y = 500Solute equation: 0.6x + 0.05y = 75To isolate a variable for substitution, we can see its easier to start with equation 1:x + y = 500 subtract y f rom both sides :x = 500 − y now substitute into equation 2 :0.6(500 − y) + 0.05y = 75 distribute the 0.6 :300 − 0.6y + 0.05y = 75 collect like terms :300 − 0.55y = 75 subtract 300 f rom both sides :− 0.55y = −225 divide both sides by − 0.55 :y = 409 ml substitute back into equation f or x :x = 500 − 409 = 91 mlSo the chemist should mix 91 ml of the 60% solution with 409 ml of the 5% solution.Further PracticeFor lots more practice solving linear systems, check out this web page: http://www.algebra.com/algebra/homework/coordinate/practice-linear-system.eplAfter clicking to see the solution to a problem, you can click the back button and then click Try Another PracticeLinear System to see another problem.Practice Set1. Solve thesystem:x + 2y = 93x + 5y = 202. Solve thesystem:x − 3y = 102x + y = 133. Solve thesystem:2x + 0.5y = −10x − y = −104. Solve thesystem:2x + 0.5y = 3x + 2y = 8.55. Solve thesystem:3x + 5y = −1x + 2y = −1247