Think about this in the next examplehow would you have done it with just one variable? 'H\2|dw7NiFqWqNr/o , .)X#2WP+T|B>G%gI%4,1LX:f>3AB,q!FURBE~e.QjayJS2#%!pEJ0gvJ*X? y y How many quarts of concentrate and how many quarts of water does Manny need? y 2 The solution (if there is one)to thissystem would have to have-5 for the\(x\)-value. + x Look back at the equations in Example 5.19. = citation tool such as, Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis. c= number of quarts of club soda. 1 x y The measure of one of the small angles of a right triangle is 14 more than 3 times the measure of the other small angle. = Hence, we get the same solution as we obtained using the substitution method in the previous section: In this example, we only need to multiply the first equation by a number to make the coefficients of the variable \(x\) additive inverses. Heather has been offered two options for her salary as a trainer at the gym. \end{align*}\nonumber\]. Solve systems of linear equations by using the linear combinations method, Solve pairs of linear equations using patterns, Solve linear systems algebraically using substitution. x & + &y & = & 7 \\ (4, 3) does not make both equations true. = How many cable packages would need to be sold to make the total pay the same? + 3 Pages 177 to 180 of I-ready math Practice and Problem Solving 8th Grade. 2 5 x+70-10 x &=40 \quad \text{distribute 10 into the parentheses} \\ Therefore (2, 1) is a solution to this system. x Well copy here the problem solving strategy we used in the Solving Systems of Equations by Graphing section for solving systems of equations. + Each point on the line is a solution to the equation. 2 2 = The latter has a value of 13,not 20.). Do you remember how to graph a linear equation with just one variable?
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