Simultaneous Equations
Math ⇒ Algebra
Simultaneous Equations starts at 8 and continues till grade 12.
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See sample questions for grade 9
A shop sells pencils and pens. 2 pencils and 3 pens cost $12. 1 pencil and 2 pens cost $7. How much does one pen cost?
A system of equations has no solution. What does this mean about the graphs of the equations?
A system of equations is given by 2x + y = 7 and 4x + 2y = 14. How many solutions does it have?
If 2x + 3y = 12 and x - y = 1, what is the value of x?
A shop sells pencils and pens. 2 pencils and 3 pens cost $12. 1 pencil and 2 pens cost $7. How much does one pen cost?
A system of equations is given by 2x + y = 7 and 4x + 2y = 14. How many solutions does it have?
A chemist needs to mix two solutions: one containing 30% salt and another containing 50% salt. How many liters of each should be mixed to obtain 10 liters of a 42% salt solution?
A school is organizing a field trip. The cost for 2 adults and 3 students is $54. The cost for 3 adults and 2 students is $62. What is the cost for one adult and one student?
If x + 2y = 8 and 2x + 4y = 16, what can you say about the system?
(1) One solution
(2) No solution
(3) Infinitely many solutions
(4) Cannot be determined
Which method is NOT commonly used to solve simultaneous equations?
(1) Substitution
(2) Elimination
(3) Graphical
(4) Multiplication
Which of the following is a consistent system?
(1) x + y = 2, x + y = 2
(2) x + y = 3, x + y = 5
(3) x - y = 1, 2x - 2y = 2
(4) x + y = 4, x - y = 2
Which of the following is a method to solve simultaneous equations?
(1) Substitution
(2) Elimination
(3) Graphical
(4) All of the above
Fill in the blank: If a system of equations has exactly one solution, the lines are ______.
Fill in the blank: If two equations are multiples of each other, the system is ______.
Fill in the blank: If two equations have the same slope but different y-intercepts, they are ______ lines.
Fill in the blank: If two equations represent the same line, the system has ______ solutions.
True or False: If two lines are parallel, their simultaneous equations have no solution.
True or False: The elimination method always requires multiplying one or both equations by a constant.
True or False: The elimination method can be used for systems with more than two equations.
True or False: The elimination method involves adding or subtracting equations to eliminate one variable.
