Download ⇥ 2 linear system of equations 1. Solve the 2 8 <

SOLVING SYSTEMS OF EQUATIONS SOLUTIONS
1. Solve the 2 ⇥ 2 linear system of equations
Solution: Consistent (2, 1)
8
< 2x y = 5 (1)
: 5x + 2y = 8 (2)
2. Solve the 2 ⇥ 2 linear system of equations
8
<
Solution: Consistent (2, 12 )
3x
: 1x
2
4y = 4 (1)
3y =
1
2
(2)
3. Solve the 2 ⇥ 2 linear system of equations
8
<
Solution: Inconsistent
:
x
y = 5 (1)
3x + 3y = 2 (2)
4. Solve the 3 ⇥ 3 linear system of equations
Solution: Consistent (1, 1, 2)
8
>
>
>
< 3x + 3y + 2z = 4 (1)
x y z = 0 (2)
>
>
>
:
2y 3z = 8 (3)
5. Solve the 3 ⇥ 3 linear system of equations
Solution: Consistent (2, 2, 2)
8
>
>
>
< 3x + 3y + 2z = 4 (1)
x 3y + z = 10 (2)
>
>
>
: 5x 2y 3z = 8 (3)
1
2
SOLVING SYSTEMS OF EQUATIONS SOLUTIONS
6. Solve the 3 ⇥ 3 linear system of equations
8
>
>
>
<
Solution: Dependent {(x, y, z) : x = 5z
x
y
x + 2y
>
>
>
:
3x
3z =
2y
2, y = 4z
z = 1 (1)
4 (2)
7z = 0 (3)
3 where z is any real number}
7. Solve the 3 ⇥ 3 linear system of equations
8
>
>
2x 3y z = 0 (1)
>
<
3x + 2y + 2z = 2 (2)
>
>
>
: x + 5y + 3z = 2 (3)
Solution: Dependent {(x, y, z) : x = 47 y + 27 , z =
13
y
7
+ 47 , where y is any real number}
8. Solve the 3 ⇥ 3 linear system of equations
8
>
>
>
<
>
>
>
:
Solution: Inconsistent
x
y
z = 1 (1)
2x + 3y + z = 2 (2)
3x + 2y = 0 (3)
9. Solve the 2 ⇥ 2 nonlinear system of equations
8
<
xy = 1 (1)
: y = 2x + 1 (2)
Solution:( 12 , 2) and ( 1, 1)
10. Solve the 2 ⇥ 2 nonlinear system of equations
Solution: (4
p
2, 4 +
p
2) and (4 +
p
2, 4
8
< y = p36 x2 (1)
:
x = 8 y (2)
p
2)
There are no Solutions. You can see this right away if you graph both equations.
The first equation is the top of a circle centered at (0,0) with radius 6 and the
second equation is a line of slope -1 and y-intercept 8. These graphs never
intersect and therefore there is no solution to the system.