Download matrix equations

Daily Practice 6L
Solve these systems of equations. Use any method on your green sheet other than Desmos.
1.
2x + 3 y = 7
x + 4y = 6
2.
-3x + 7 = y
4 y + 12x = -8
3.
4x - 2 y = 6
6x - 3 y = 9
Write these systems of linear equations as augmented matrices and matrix equations.
System
Augmented Matrix
Matrix Equation
A
ì x - 2 y = 5 - 3z
ïï
í -3x - 9z + 6 y = -15
ï 4x - 20 = 8 y - 12z
ïî
B
ì 6x - 2 y + z = 10
ïï
í x+ y+ z= 1
ï -7x + 5 y - 3z = 1
ïî
C
ì 20 = 6x + 2 y + 18z
ïï
í 2 y + 14z = 14 - 4x
ï -x + 3 y + 7z = 0
ïî
D
ì x + 2 y + 5z = 4
ïï
í 2x + 4 y + 10z = 20
ï -3x - 6 y - 15z = 4
ïî
FRAMEWORK AND PARTIAL SOLUTIONS
3 systems of 2 equations, 2 unknowns:
1. Intersecting lines: one solution at (2,1)
2x + 3 y = 7
x + 4y = 6
2. Parallel lines: no solution
-3x + 7 = y
4 y + 12x = -8
3. Coincidental lines: infinite solutions
4x - 2 y = 6
6x - 3 y = 9
4 systems of 3 equations, 3 unknowns:
A
B
C
D
System
ì x - 2 y = 5 - 3z
ïï
í -3x - 9z + 6 y = -15
ï 4x - 20 = 8 y - 12z
ïî
ì 6x - 2 y + z = 10
ïï
í x+ y+ z= 1
ï -7x + 5 y - 3z = 1
ïî
ì 20 = 6x + 2 y + 18z
ïï
í 2 y + 14z = 14 - 4x
ï -x + 3 y + 7z = 0
ïî
ì x + 2 y + 5z = 4
ïï
í 2x + 4 y + 10z = 20
ï -3x - 6 y - 15z = 4
ïî
Augmented Matrix
all equations are
multiples of each
other: infinite
solutions, coincide
on one plane
Consistent: single
solution (3, 2, -4)
Infinite solutions;
intersects at a line
formed by 2 planes
RREF:
1023
0131
0000
parallel planes; no
solutions
Matrix Equation