Simultaneous Equations
Math ⇒ Algebra
Simultaneous Equations starts at 8 and continues till grade 12.
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See sample questions for grade 11
A shop sells pens and pencils. A pen costs $2 and a pencil costs $1. If a student buys 3 pens and 4 pencils for $10, and another student buys 2 pens and 6 pencils for $10, how much does each item cost?
Describe the graphical representation of a system of equations that has infinitely many solutions.
Given the system:
2x + 3y = 13
3x - 2y = 4
Find the values of x and y.
Given the system:
2x + y = 7
4x + 2y = 14
How many solutions does this system have?
Given the system:
3x - 2y = 7
5x + y = 13
Find the value of y.
A shop sells pens and pencils. A pen costs $2 and a pencil costs $1. If a student buys 3 pens and 4 pencils for $10, and another student buys 2 pens and 6 pencils for $10, how much does each item cost?
A chemist needs to mix three solutions containing 10%, 20%, and 30% acid, respectively, to obtain 100 mL of a solution that is 22% acid. If the amount of the 10% solution used is twice the amount of the 30% solution, set up the system of equations representing this situation and solve for the amount of each solution used.
A company produces two products, A and B. Each unit of A requires 2 hours of labor and 3 units of raw material. Each unit of B requires 1 hour of labor and 4 units of raw material. If the company has 100 hours of labor and 180 units of raw material available, and must produce at least 10 units of A, set up the system of equations and inequalities representing this situation.
If a system of equations has no solution, it is called:
(1) Consistent
(2) Inconsistent
(3) Dependent
(4) Homogeneous
Which of the following is a necessary condition for a system of two linear equations to have a unique solution?
(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 method for solving simultaneous equations?
(1) Substitution
(2) Elimination
(3) Multiplication
(4) Graphical
Which of the following methods can be used to solve a pair of simultaneous linear equations?
(1) Substitution method
(2) Elimination method
(3) Graphical method
(4) All of the above
A system of equations is called ______ if it has exactly one solution.
A system of equations is said to be ______ if it has no solution.
Fill in the blank: If the determinant of the coefficient matrix of a system of two equations is zero, the system is either ______ or inconsistent.
Fill in the blank: If the ratio of the coefficients of x and y in two equations is equal, but the ratio of the constants is not, the system is ______.
True or False: Every system of two linear equations in two variables has exactly one solution.
True or False: The elimination method always requires multiplying one or both equations by a constant.
True or False: The solution to a system of equations is the point where their graphs intersect.
True or False: The substitution method can only be used if one equation is already solved for one variable.
