CAT
Chapter 8A Review
Name:
Decide whether the ordered pair is a solution of the given system.
1) x + y = 8
2) x + y = -2
x - y = -2 ; (-3, 5)
x - y = -8 ; (-5, 3)
Determine whether the system of equations is consistent or inconsistent. If the system is
consistent, determine whether the equations are dependent or independent.
3) x + y = 2
4) 2x - y = 4
x+y=5
x + 3y = 2
5) 2x - y = 5
-4x + 2y = -18
Solve the system of equations by the substitution method. Check your solutions. For any
dependent equations, write your answer in the ordered pair form.
6) 5x - 2y = -1
x + 4y = 35
7) x = -33 - 8y
6x + 7y = 7
Solve the system of equations by the elimination method. Check your solutions. For any
dependent equations, write your answer in the ordered pair form.
8) x - 4y = -4
-4x - 3y = -3
9) x + 4y = 13
2x + 3y = 6
Determine whether the ordered triple is a solution to the given linear system.
10) (-2, -1, 5)
11) (-3, -1, 4)
x- y+ z= 4
2x - 2y - 3z = -16
2x - 8y - 3z = 24
4x - 3y + 3z = 3
3x + 4y + 2z = 7
x + y - 5z = -24
Solve.
12) x - y + z = 6
13) x - y + z = 2
2y + z = 8
3y + z = 12
z=4
z=6
Solve the system of linear equations. If the equations are dependent, write your answer
with z being arbitrary.
14) x + y + z = 7
15) x - y + z = 8
x - y + 2z = 7
x+y+z=6
5x + y + z = 11
x + y - z = -12
Determine if the given ordered pair is a solution to the system of equations.
16) x2 + y2 = 9
y = x – 3 ;(0, -3)
17) y = x2
y = x + 2 ;(0, 2)
Solve the system of equations by the substitution method. Check your solutions.
18) x2 + y2 = 13
x + y = -5
19) y = x2 - 14x + 49
x + y = 27
Solve the system of equations (only real solutions) by the elimination method. Check your
solutions.
20) y = 3x2 + 6x
y = x2 - 4x + 12
21) 2x2 - 4y2 = -28
3x2 + 4y2 = 48
Determine if the given ordered pair is a solution to the system of inequalities.
22) x + 3y ≥ 0
23) x + 3y ≥ 0
2x + y ≤ 10
2x + y ≤ 10
y ≥ 0;
y≥0;
(-2, 2)
(7, 4)
Graph the solution set of the system of linear inequalities and label the vertices (if any) of
the solution set.
24) 3x + 2y ≤ -6
x-1≥0
25) x + 2y ≤ 2
x+y≥0