1.3 Solving Systems by Substitution

Steps for Substitution

1.Solve for the “easiest” variable2.Substitute this expression into

the other equation3.Solve for remaining variable4.Substitute the value into the

starting equation to solve for final variable

5.Write as ordered pair and check

Solve by Substitution 3X + Y = 818X + 2Y = 4

Show me how to solve by Show me how to solve by

SubstitutionSubstitution!!!! X = Y + 32X + 2Y = 2

Steps for Elimination

1.Line up the equations.2.Look to see if you add the “columns” if

either variable is eliminated.3.If it isn’t, look to see what you could

multiply by to eliminate a variable.4.Rewrite the equation you need to multiply

and multiply the whole equation by that number.

5.Rewrite the other equation under it.6.Add the “columns.”7.Solve for that variable.8.Substitute that answer into one of the

original equations and solve for the other variable.

9.Write it as an ordered pair.

Solve by Solve by EliminationElimination2X + Y = 82X + Y = 8

X – Y = 10X – Y = 10

Solve by Elimination 3X + Y = 818X + 2Y = 4

Solve by Elimination X + Y = 42X + 3Y = 9

2X – 4Y = 5–X + 2Y = 8

Solve by Elimination

Solve by Elimination 4Y + 30 = 10X 5X – 2Y = 15

– – 4.5x + 7.5Y = – 94.5x + 7.5Y = – 9

3x – 5Y = 63x – 5Y = 6

Multiply by ten to eliminate Multiply by ten to eliminate decimals.decimals.

– – 45X+ 75 Y= – 9045X+ 75 Y= – 90

3X – 5Y = 63X – 5Y = 6

Yuck!!

17 2

22 4

y x

y x

2x – 3y + 4z = 83x + 2y = 7x = 1

What size is the system?

Let’s look at Page 15 # 22Let’s look at Page 15 # 22Take the words and build a system of equations.

AssignmentAssignment