Systems

 __System of Equations__// 

 System of Equations can

be solved by Graphing, Substitution, and by

Elimination

Word Problems

 I'll use " //t// " for the "tens" digit of the original number and " //u// " for the "units" (or "ones") digit. Keeping in mind that the tens digit stands for "ten times this value", I then have:  //t// + //u// = 7  10  //u// + //t// = 10 //t// + //u// + 27  (The " 10 //t// + //u// " on the right-hand side of the second equation represents the original number.) First I'll simplify the second equation:  10 //u// + //t// = 10 //t// + //u// + 27 9  //u// – 9 //t// = 27  //u// – //t// = 3  <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff">This gives me: <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff"> //u// + //t// = 7 <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff"> //u// – //t// = 3 <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff"> Adding down, I get 2 //u// = 10, so //u// = 5. Then //t// = 2. Checking, this means that the original number was 25 and the new number (gotten by switching the digits) is 52. Since 52 – 25 = 27, this solution checks out. Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff"> **The number is** **25** **.** <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff">__ Graphing __  <span style="FONT-SIZE: 200%; COLOR: #ffffff; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #827c9c"> <span style="FONT-SIZE: 200%; COLOR: #ffffff; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #827c9c"> <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff"> <span style="FONT-SIZE: 200%; COLOR: #ffffff; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #827c9c"> media type="custom" key="783155" <span style="DISPLAY: block; FONT-SIZE: 200%; COLOR: #ffffff; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #5f5c7f; TEXT-ALIGN: left"><span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff">
 * <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff">
 * <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff">
 * <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff">
 * <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff">
 * <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff">
 * <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff">
 * <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff">
 * <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff">
 * <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff">
 * <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff"> ** The sum of the digits **
 * <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff">
 * <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff"> **of a two-digit number is** **7** **. When the digits are reversed, the number is increased by** **27** **. Find the number.**
 * <span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff"> **of a two-digit number is** **7** **. When the digits are reversed, the number is increased by** **27** **. Find the number.**

<span style="FONT-SIZE: 200%; COLOR: #ffffff; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #827c9c">

<span style="FONT-SIZE: 200%; COLOR: #ffffff; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #827c9c"><span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff"> <span style="FONT-SIZE: 200%; FONT-FAMILY: 'Comic Sans MS', cursive"> Solving Systems

with <span style="FONT-SIZE: 200%; COLOR: #ffffff; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #827c9c"><span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff"> <span style="FONT-SIZE: 200%; FONT-FAMILY: 'Comic Sans MS', cursive">

Substitution

media type="custom" key="783285"

<span style="FONT-SIZE: 150%; COLOR: #4d3d3d; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #ffffff"> <span style="FONT-SIZE: 200%; COLOR: #ffffff; FONT-FAMILY: 'Comic Sans MS', cursive; BACKGROUND-COLOR: #8b8ca7">__ Solving Systems of

Linear

Inequalitie

__ media type="custom" key="783119"