Download Chapter 8 System of Equations Review

Math 11
Systems of Equations Review
Name: _________
Block: _________
Show ALL your work.
1.
Transform into y=mx +b and graph
y + 4 = -2x
2.
Determine the number of solutions (0,1, or many…)? Explain your answer.
2y + 6x2 + x -8 = 0
3y + x -12 = 0
3.
Describe the difference between a system of equations with two solutions
and no solutions in terms of the graph.
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4.
a)
Solve by graphing – show the checks.
y – x2 + 2x + 4 = 0
y- 3x + 8 =0
Check:
b)
y- 3x2 – 12x = 6
y + 4x2 + 16x = -15
5.
Solve by substitution.
a)
4x + y = 5
b)
5x – 2y = 16
c)
2x2 – y +16x + 29 = 0
-2x2 – 16x – y = 35
4x2 – y – 2x = -7
-6x – y + 15 = 0
d)
3x2 – y – 4x = -3
-2x2 + 2x – y +8 = 0
6.
Solve by elimination.
a)
2(x - 1) + y = 2
b)
y = x2 + 2x – 6
3x – 4(y + 3) = 5
c)
t = -3d2 – 2d + 3.25
t = (1/8)d – 5
y = -6x2 – 4x + 7
d)
2y – 1 = x2 - x
x2 + 2x + y – 3 = 0
7. Solve the system of equations and check.
3x + y –z = 8
2x – y + 4z = -12
6x – 2y + 3z = -7
8.
9.
Determine two whole numbers such that the first number increased by triple
the second number is 24. If the first number is squared and decreased by
five times itself, the result is 13 less than the second number.
The approximate height, h, in metres, travelled by golf balls hit with two
different clubs over a horizontal distance of d metres is given by the
following functions:
Seven-iron: h(d) = -0.002d2 + 0.3d
Nine-iron: h(d) = -004d2 +0.5d
a) At what distance is the ball at the same height when either club is used?
b) What is the height