Problem Set 1 : Equations and Inequalities with Two Variables
4:45 AM
Muhammad Yusuf
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1. Sketch the inequality x + 2y < 4
2. Sketch the inequality 5x + 2y ≥ -10
3. John
and Mary wrote a Math test. Two times John's score was 60 more than Mary's
score. Two times Mary's score was 90 more than John's score. Determine their
two scores.
4. Sketch
the equations 4x - y = 8 and 2x - 3y = 2 on the same graph. Find the point of intersection of the two lines.
5. Sketch the points that
satisfy:
3x + y ≥ 12
x - y ≤ 4
2x - 3y ≤ 6
6. Sketch the points that
satisfy:
2x + y > 4
x ≥ 2
x + y < 5
7. A
company makes cars and trucks. In any given week, a total of up to 400 vehicles
can be made. Draw a graph showing the number of cars and trucks that could be
made in one week.
8.
Michael plans to spend up to 12 hours reviewing Science and Math in preparation
for examinations. Michael is not as good in Science as he is in Math, so he
wants to study at least two times more for science then he does for math. Draw
a graph showing how much time she could spend studying each subject.
9. Find the area of the
triangle enclosed by the lines -4x+3y = 5, 3x+2y = 43 and -5x+8y = 19.
10. If the system of
equations
px + qy = 8
3x - qy = 38
has the
solution (x, y) = (2, -4). Determine p and q.
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