System — Grade 8 Math, what it means and where it is taught
Two or more equations that must hold at the same time.
Taught in Grade 8 Math.
Where it is taught
What uses it later
This idea is needed for:
- Feasible region — The shaded overlap for a system of inequalities.
Practise this idea
4 questions in the course bank use System, in Systems of Linear Equations, Systems of Equations & Inequalities, Matrices & Systems.
Problem 1
Two lines cross at (5, -2). What is the solution of the system?
Worked answer
(5, -2)
The crossing point satisfies both equations
(5, -2)
Problem 2
A system of two linear inequalities has a solution region shaped like a wedge. This means
- the two boundary lines cross
- the lines are parallel
- there is no solution
- the lines are the same
Worked answer
the two boundary lines cross
Crossing lines cut the plane into four wedges
The solution is one of them
Problem 3
For the system 2x+3y=7, 4x+6y=1, find the determinant of the coefficient matrix.
Worked answer
0
2(6)-3(4) = 0
So there is no unique solution
Problem 4
A system has coefficient determinant 0 and the equations are not multiples of each other. How many solutions?
- None
- Exactly one
- Infinitely many
- Two
Worked answer
None
The lines are parallel and distinct
Parallel lines never meet