ࡱ> ~ ,bjbjcTcT >>}<<L^):cccc:::ALCLCLCLCLCLCL OQCL9:8:::CLcca#|L<<<:lccAL<:AL<<iJ|q,Kc:@J-LL0LJHR:HR$KHRKL::<:::::CLCLv<:::L::::HR::::::::: : Solving Linear Systems with Graphing-7.1  Definition: A Linear System is a set of two linear equations. Example: y = -2x and y = x + 3 Does the point (0, 4) make either equation true? Substitute it in and find out. Does the point (2, 5) make either equation true? Explain. Does the point (-1, 2) make either equation true? Explain. If a point works in both equations of a linear system, then that point must be the SOLUTION to the linear system. When you solve a linear system you find that one point makes both equations true. What point is the solution to the system above? ____________ Plot both equations in the same coordinate plane below. y = -2x and y = x + 3  At what point do the two lines intersect? _________ Compare this with your answer for #4 An ordered pair that makes a linear equation TRUE is called a __________________. The point that the two lines ________________ is the solution to the system! To solve a system of linear equations, the ordered pair must work for ______ equations!   Example: y = 2x Point________ y = "x + 3 Verify:  Example: y - 2x = " 4 Point________ y = x " 2 Verify: Try these:  EMBED Equation.DSMT4  2.  EMBED Equation.DSMT4  3.  EMBED Equation.DSMT4   7.1 Solving Systems of Equations by Graphing Homework Solve these linear systems by graphing. y = -x + 3 and y = 2x 6 2) y = -x + 3 and y = x + 1   3) x y = 2 and x + y = -6 4) x + y = -2 and 7x 4y = 8    Steps for Solving a Linear System Using Graphing: Put the equations in slope-intercept or standard form. *+,9klz{~) + > ? @ A k l m thtthtYhhlhLCJOJQJaJhlCJOJQJaJhLCJOJQJaJhlhlCJOJQJaJhlCJOJQJaJhLCJOJQJaJhlhlCJOJQJaJhlhlOJQJhlCJaJhl5CJaJhlOJQJ"jh|OJQJUmHnHuhljhlCJUmHnHu *,kl) * + , k l m 2 3 r gdl^gdl & Fgdlgdlm 1 2 3 r w | 5 6 󿥝xlx`Qh$h_CJOJQJaJhLCJOJQJaJhlCJOJQJaJhlhlCJOJQJaJ+jhlhl5OJQJUmHnHuhLOJQJhlhlOJQJhlhlCJOJQJaJhl5OJQJhlhl5>*OJQJhlhl56OJQJhlhl56>*OJQJhlhl5OJQJ 6 7 ` b $O&`#$/Ifgd$ & Fgd$gdlb d h j l n p r t v x |  $a$gd$vkd$$Ifl      c'' t 6`O0      644 layt$6 d f h j l p x z |  " : < D N R T ^ ų؟؊ŊŊ{lYlC+jP hq/5CJOJQJUV\aJ%jhq/5CJOJQJU\aJhq/5CJOJQJ\aJhl5CJOJQJ\aJhLOJQJhlOJQJmHnHu&jhlCJOJQJUmHnHu"jh_OJQJUmHnHuh_OJQJh_h$OJQJhlOJQJ/jh_h$>*OJQJUmHnHtHuh$OJQJ        " z | JNOPQRST & F>^`>gdq/ %&'(./FGHIJMUůŁi]KChlOJQJ"jhq/OJQJUmHnHuhq/CJOJQJaJ/j:hq/hq/5CJEHOJQJU\aJ+jP hq/5CJOJQJUV\aJ/jhq/hq/5CJEHOJQJU\aJ+jP hq/5CJOJQJUV\aJhq/5CJOJQJ\aJ%jhq/5CJOJQJU\aJ/jhq/hq/5CJEHOJQJU\aJTU     de^gdf8gd_*^*gd1) & Fgdf8h^hgd_gdq/UV˾xxii]iDD0jh1)h|CJOJQJUaJmHnHuh_CJOJQJaJh1)h1)CJOJQJaJhPCJOJQJaJh1)CJOJQJaJh1)h_CJOJQJaJh1)hf8CJOJQJaJh1)h1)5CJOJQJaJh_5CJOJQJaJh1)h_5CJOJQJaJh|5CJOJQJaJ-jh|5CJOJQJUaJmHnHu%'89<=@Bcegiknoyz{|}ǻ⯖zeVD"h_h|5>*CJOJQJaJhTh|CJOJQJaJ(jhThTCJUaJmHnHuj hTCJOJQJUaJh_CJOJQJaJ0jh1)h|CJOJQJUaJmHnHuh|CJOJQJaJh(CJOJQJaJh1)CJOJQJaJh1)h1)CJOJQJaJh1)h_CJOJQJaJh1)hf8CJOJQJaJeghilmnopqrstuvwxy{}3,g,, $ & Fa$gd_$a$gd_$a$gdT^gdf8,,,,,,,,,,,ƷhTh|CJOJQJaJhf8h$'h|CJHOJQJaJHh|CJHOJQJaJHh|Uh_h|OJQJh|>*OJQJ Graph each equation on the same coordinate system. 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