Download 13_5elimination method by multiolication

13-5
• Objective: Solve system equations by the
elimination method using multiplication and
division
Questions to consider
When do we use the multiplication method
in order to eliminate a varriable?
What steps are needed in oder to complete
the process?
x  4 y  17
3x  2 y  9
Previously, we learned how to solve systems of equations by using addition or
subtraction which eliminated one of the variables.
2x  3 y  12
x  3y  6
3x  2 y  15
3x  y  9
This system of equations could be solved by eliminating
the y variable through addition.
This system of equations could be solved by
eliminating the x variable through subtraction.
Since this system of equations can’t be solved by elimination with addition or
elimination with subtraction, how can we solve it?
x  4 y  17
3x  2 y  9
If the top equation was multiplied by 3,
then the first term would be -3x. The
bottom equation could then be subtracted
from the top equation eliminating the
variable x.
x  4 y  17
3x  2 y  9
Previously, we solved this system of
equations by multiplying the top equation
by 3 and then used elimination by
subtraction.
Could we have used a different factor for the multiplication?
1.
Arrange the equations with like terms in columns.
2.
Multiply one or both equations by an appropriate factor so that the new
coefficients of x or y have the same absolute value.
3.
Add or subtract the equations and solve for the remaining variable.
4.
Substitute the value for that variable into one of the equations and solve
for the value of the other variable.
5.
Check the solution in each of the original equations.
4x  3 y  12
x  2 y  14
Multiply the bottom equation by 4 to get a new
system of equations.
Subtract the bottom equation from the top equation.
Solve for y.
Solve for x by substituting the value
for y into one of the equations.
4x  3 y  12
x6
y4
x  2 y  14
Check the solution by substituting the values for the variables into
each equation.
4 x  3 y  12
4 6  3 4  12
24  12  12
12  12 
x  2 y  14
6  2 4  14
6  8  14
14  14 
This system of equations represents two lines which intersect at the point (6,4).
16x  8 y  12
12x  6 y  9
The lowest common multiple of 6 and 8 is 24. Multiply
the top equation by 3 and the bottom equation by 4.
The new system of equations is:
2x  4 y  3
3x  6 y  8
The lowest common multiple of 2 and 3 is 6.
Multiply the top equation by 3 and the bottom
equation by 2.
Add the new system of equations
together.