Download 2 - Algebra House

Mr. Sims
Solve the system of equations.
1. x + 2y + 5z = -1
2x – y + z = 2
3x + 4y – 4z = 14
1.) choose two equations
and eliminate one variable
x + 2y + 5z = -1
2 2x – y + z = 2
x + 2y + 5z = -1
4x – 2y + 2z = 4
5x + 7z = 3
2.) choose a different pair
of equations and eliminate
the same variable {y}
4 2x – y + z = 2
3x + 4y – 4z = 14
Algebra 2
Section 10.3 B
Solving Systems of
Three Linear Equations
4.) keep substituting until
all variables are solved for
substitute 2 in for x into the
equation with x and z
5x + 7z = 3
5(2) + 7z = 3
10 + 7z = 3
-10
8x – 4y + 4z = 8
3x + 4y – 4z = 14
11x = 22
x=2
y and z were eliminated,
x is solved for, go to step 4
-10
7z = -7
z = -1
substitute x and z into an
equation with x,y, and z
x + 2y + 5z = -1
2 + 2y + 5(-1) = -1
2 + 2y – 5 = -1
2y – 3 = -1
+3 +3
2y = 2
y=1
Mr. Sims
2. 5x – 4y + 4z = 18
-x + 3y – 2z = 0
4x – 2y + 7z = 3
3.) use the two new equations
to solve for a variable
11y – 6z = 18
-6 10y – z = 3
1.) choose two equations
and eliminate one variable
5x – 4y + 4z = 18
5 -x + 3y – 2z = 0
5x – 4y + 4z = 18
-5x + 15y – 10z = 0
11y – 6z = 18
2.) choose a different pair
of equations and eliminate
the same variable {x}
4 -x + 3y – 2z = 0
4x – 2y + 7z = 3
- 4x + 12y – 8z = 0
4x – 2y + 7z = 3
10y – z = 3
5x = 30
x=6
11y – 6z = 18
-60y + 6z = -18
-49y = 0
y=0
4.) keep substituting until
all variables are solved for
substitute 0 in for y, into any
equation with y and z
10y – z = 3
10(0) – z = 3
-z = 3
z = -3
substitute 0 in for y and -3 in for z
into any equation with x,y, and z
5x – 4y + 4z = 18
5x – 4(0) + 4(-3) = 18
5x – 12 = 18
+12
+12
Mr. Sims
3.
-5x + 3y + z = -15
10x + 2y + 8z = 18
15x + 5y + 7z = 9
3.) use the two new equations
to solve for a variable
1.) choose two equations
and eliminate one variable
2 -5x + 3y + z = -15
10x + 2y + 8z = 18
-10x + 6y + 2z = -30
10x + 2y + 8z = 18
8y + 10z = -12
4.) keep substituting until
all variables are solved for
8y + 10z = -12
8(- 4) + 10z = -12
-32 + 10z = -12
2.) choose a different pair
of equations and eliminate
the same variable {x}
3 -5x + 3y + z = -15
15x + 5y + 7z = 9
-8y – 10z = 12
14y + 10z = -36
6y = -24
y=-4
-1 8y + 10z = -12
14y + 10z = -36
-15x + 9y + 3z = - 45
15x + 5y + 7z = 9
14y + 10z = -36
+32
10z = 20
z=2
10x + 2y + 8z = 18
10x + 2(- 4) + 8(2) = 18
10x – 8 + 16 = 18
10x + 8 = 18
-8
x=1
+32
-8
10x = 10
Mr. Sims
Algebra 2
Section 10.3 B
Assignment
Solve each system of equations.
1.) 2m + 2n + 6p = 9
m – 3n + 2p = 5
-m – 5n – 4p = 4
2.) x + 3y + 2z = 11
4x + 2y + 5z = 15
-2x + 3y – z = 5
Mr. Sims
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Mr. Sims