∙ The solutions to a system of equations are the points of intersection of the graphs. ∙ For a system consisting of two linear equations:
There are 3 cases to consider:
State whether each of the following systems have ONE, NONE, or INFINITE solutions
i) 3x + y = 7 4x + y = 7
ii) 6x + 2y = 10 3x + y = 5
iii) x - y = 3
3x - 3y = 6
Find a value for c that will give the following system: 3y + 2cx = 6 y - 6x = 0
i) one solution
ii) no solutions
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Depending on whether and how the linear equations in a system touch each other, there will be different number of solutions to the system. There can be one solution, no solution and even infinite solution.
