Homework unit 5 systems of equations & inequalities answer key

Unit 5: Systems of Equations ALL NotebooksMarch- April 20215.01 Foundations (1 dayLesson)To receive full credit on this notebook you will need to fill in all parts and SHOW YOUR WORKDistributive PropertyMultiply a sum by multiplying each _______________separately and then add the products.a(b + c) = ab + ack(m – n) = km - knExamples: Use the distributiveproperty to simplify the following:1)7(y + 2) =2)3(6x – 5) =Practice by distributing:1)2)3)2 (20 – 4a)4)Combining Like Terms1)Group _________________ together.Example: 4x + 5x = (4+5)x = 9xExamples: Combine the like terms ineach expression:1)3m – m + 4m =2)5jk + 13 – 3jk – 7 =3)2y + 6z – 6y + 2z =Identify Like Terms:1)6c, 2d, 6d, 5c, -22)12a, -4b, -2a, 8abSimplify by combining like terms:1)8j -12 + 9j – 42)a + 4a – 6y + 5 + 7yPage1of23

Unit 5: Systems of Equations ALL NotebooksMarch- April 20213)3x, -8xy, 4y, 7, 6xy, -34)5wz, –3w, 6z, wz, 3z3)4t + 6 – 2m – 2t + 7Put it all together!Simplify completely:1)2)3)4)5.02 Systems of Equations****Vocab ****System of Equations -a set of two or more equations with the same variables.Consistent: A system of equations withEXACTLY ONE solution. Intersects at one point.Consistent Independent/Coincident:A system of equations with INFINITELY MANY solutions. Sameline.Inconsistent:A system of equations with NO solutions. Parallel linesPage2of23

Unit 5: Systems of Equations ALL NotebooksMarch- April 2021Review: Converting to Slope Intercept FormConvert to Slope-Intercept Form:12x + 2y = 8Finding Solutions with GraphsGraph the LinearEquations below:y = 2x - 3y = -x + 4What is the pointwhere the twographs cross?

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Unit 5: Systems of Equations ALL NotebooksMarch- April 2021(0,0)(-2,0)(-2,2)(0,-4)The system has no solution.(0,0)(-6,0)(0,2)(2,0)The system has no solution.System of EquationsA collection of two or moreequations that are graphed onthe same plane.The solution is:-No Solution (when the equationsnever cross)-One Solution (when the twoequations cross)-Infinite Solutions (when theequations line up exactly)How to tell how many solutions systems of equations have using the equations!y = -x + 1 and y = -x -3y = .5x + 3 and –x + 2y = 6-Rearrange to y = mx+bConsistent IndependentA system of equationswithEXACTLY ONE solution.Intersects at onepointPage4of23

Unit 5: Systems of Equations ALL NotebooksMarch- April 2021Coincident (ConsistentDependent)A system of equationswithINFINITELY MANYsolutions.Same lineInconsistentA system of equationswithNO solutions.Parallel linesPage5of23

Unit 5: Systems of Equations ALL NotebooksMarch- April 2021Prove it: Show your work and putyour answer here:5.03 Approximating Solutionswith GraphsSolving Systems by GraphingThe Steps!

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