Stage Step of process Specific Example - Fill in the Blanks Given a system of two linear equations with two variables, f

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Stage
Step of process
Specific Example - Fill in the Blanks
Given a system of two linear equations with two
variables, find the set of solutions (x,y)
Solve the system
x=y+3
4=3x-2y
Substitution Method
1. Solve one of the equations for either of the
variables
The top equation is already solved for x
2. Substitute the result into the other
equation
Substituting in the bottom equation
4=3 -2y
3. Solve the resulting equation
y= -5
4. Substitute the result of step 3 into the equation
found at the end of step 1
Substituting y= -5into
x=y+3
Addition Method
(Elimination Method)
5. Format the system so you can add the
equations
Ax+By=C
Dx+Ey=F
x-y=3
3x-2y=4
6. Multiply every term in one or both equations so that
the coefficients of one of the variables are opposites
Multiplying the top equation by ___
3x-2y=4
7. Add the equations to eliminate one of the
variables
Adding the equations we get
8. Divide to solve the equation from step 7
Dividing by ___
9. Substitute the result of step 8 into either of the
given equations
Substituting
Graphing Method
10. Put both equations in slope intercept
form
y=m1x+b1
y=m2x+b2
x-y=3y=x-3
3x-2y=4y=32x-2
11. Graph each equation using the methodology for
graphing linear functions and identify the intersection point x,y
of the two lines
Validation
12. Check the solution by substituting into both of the
original equations in the system
Substituting
( )=( )+3
4=3( )-2( )
Stage
Step of process
Specific Example - Your Turn
Given a system of two linear equations with two
variables, find the set of solutions (x,y)
Solve the system
3x-18=2y
-10=5x+10y
Substitution Method
1. Solve one of the equations for either of the
variables
2. Substitute the result into the other
equation
3. Solve the resulting equation
4. Substitute the result of step 3 into the equation
found at the end of step 1
Addition Method
(Elimination Method)
5. Format the system so you can add the
equations
Ax+By=C
Dx+Ey=F
6. Multiply every term in one or both equations so that
the coefficients of one of the variables are opposites
7. Add the equations to eliminate one of the
variables
8. Divide to solve the equation from step 7
9. Substitute the result of step 8 into either of the
given equations
Graphing Method
10. Put both equations in slope intercept
form
y=m1x+b1
y=m2x+b2
11. Graph each equation using the methodology for
graphing linear functions and identify the intersection point x,y
of the two lines
Validation
12. Check the solution by substituting into both of the
original equations in the system