System of Equations 2
 Solving Using Substitution where the lines intersect.  So the solution could bewhich of the following?A solution to a system of equations isA single point (one ordered pair)No solution (parallel lines; they don't intersect)Infinite # of Solutions (same line)all of the above 1. Solve for the other variable.2. Substitute the # or expression in forthe isolated variable.4. Isolate one of the variables.3. Take the answer you got, and plug it into one of the equations to find the othervariable.5. Write the ordered pair.Put the steps in order for solving a system  using the method of substitution.4, 2, 1, 3, 51, 4, 2, 3, 52, 1, 4, 3, 54, 3, 2, 1, 5 {Solve by Substitution.    Fill in the blanks. 3x - 1 = 2x - 1 = 5y = 3x - 1y = x + 52x = 6x = 3Answer (y = 3 •y = y = 89 - 1,- 1) Solve by substitution.  Fill in the blanks.2           + 3y = 21   {y = (2x + 3y = 21x = 9)So, the solution is (,) Solve by substitution.  Fill in the blanks.{y = -2x + 1y = 4x - 5= 4x - 5(,) Step 1:  Solve for x in the 2nd equation.Step 2:  Substitute the expression into the otherequation.Solve by Substitution.  Fill in the blanks.Step 3:  Solve for y!x = -2y - 1{y = 3x - 2y = 13x + 2y = -13()- 2y = 13Step 5:  Write the ordered              pair.Step 4:  Substitute the  y value into either equation.The solution is:(,) Solve the system.{y = 4x + 2y = 10Answer:(,) Is (-4, -1) a solution of{3x - 2y = -105x - 11y = -9?yesno Solve the system.{2x - y = 1y = 10Answer:(,) Solve the system.{4x -2y = 10x = 4Answer:(,) Solve the system.{y = -5x + 15x + 2y = 7Answer:(,) What would be the first step when solvingthis system using substitution?Substitute (7x - 5y) for x in the first equationSubstitute (x + 3) for y in the second equationSubstitute (y + 3) for y in the second equationSubstitute (y + 3) for x in the second equation{x = y + 37x - 5y = 19 There is no next step.      You are done.Plug -3 in for x into     either original equation    to find yWhat would the next step to find the solution?{-2x - y = -2y = x - 1Plug 1 in for y into either    equation to find xPlug 1 in for x into either   original equation to find y -2x - (x - 1) = -2-3x + 1 = -2-3x = -3x = 1 (This means theyare parallel lines!)When our variables disappear and we are leftwith a false statement, the answer is "no solution". (This means theyare completely overlapping!)When our variables disappear and we are leftwith a true statement, the answer is "infinitely many".Infinitely many4x - 2y = 4y = 2x - 24x - 2(2x - 2) = 44x - 4x + 4 = 44 = 4 Solve the system.{4x -2y = 10y =2x +5Infinitely manyNo solution Solve the system.{3x+ y = 6y = -3x + 6Infinitely manyNo solution
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