Simultaneous Equations
Math ⇒ Algebra
Simultaneous Equations starts at 8 and continues till grade 12.
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See sample questions for grade 12
A shop sells pens and pencils. 3 pens and 2 pencils cost $11, while 2 pens and 3 pencils cost $10. Find the cost of one pen and one pencil.
A system of equations is given by: 2x + 3y = 13, 4x - y = 5. What is the value of y?
A system of equations is given by: x + 2y = 8, 3x - y = 7. What is the value of x?
Explain the difference between a consistent and an inconsistent system of equations.
Given the system: 3x - 2y = 4 and 5x + y = 13, find the value of y.
Given the system: 4x + 5y = 9, 2x - 3y = 1, solve for x.
Given the system: x + 2y + 3z = 14, 2x - y + z = 5, x - y + z = 6, solve for y.
A shop sells pens and pencils. 3 pens and 2 pencils cost $11, while 2 pens and 3 pencils cost $10. Find the cost of one pen and one pencil.
If a system of two linear equations has no solution, what can be said about the lines represented by the equations? (1) They are parallel (2) They intersect at one point (3) They coincide (4) They are perpendicular
Which method is most suitable for solving a system of equations with three variables? (1) Substitution (2) Elimination (3) Graphical (4) Both (1) and (2)
Which of the following is a necessary condition for a unique solution in a system of two linear equations in two variables? (1) The lines are parallel (2) The lines coincide (3) The lines intersect at one point (4) The lines are perpendicular
Which of the following is NOT a possible outcome when solving a system of two linear equations? (1) One solution (2) No solution (3) Two solutions (4) Infinitely many solutions
Fill in the blank: If two equations in a system are multiples of each other, the system is said to be ______.
Fill in the blank: The ______ of a system of equations is the number of solutions it has.
Fill in the blank: The elimination method involves adding or subtracting equations to ______ one of the variables.
Fill in the blank: The point of intersection of two non-parallel lines in a plane represents the ______ of the corresponding simultaneous equations.
True or False: If the graphs of two equations coincide, the system has infinitely many solutions.
True or False: The graphical method can be used to solve systems of equations with more than two variables.
True or False: The substitution method is always the most efficient way to solve simultaneous equations.
True or False: The system of equations x + y = 4 and 2x + 2y = 8 has infinitely many solutions.
