Question

Explain what “solution” means for a system of two linear equations. Give an example.

Answer 1

Explanation:

In this context "solution" means a point whose x- and y-coordinates satisfy both equations.

If we're given the two linear equations x + y = 3 and 2x - y = 7, we can solve them by addition and subtraction (among other methods):

3x = 3 + 7, or 3x = 10, or x = 10/3.

Substitute this result into x + y = 3 to find the corresponding y value;

10/3 + y = 3, or 10/3 + y = 9/3, or y = 1/3.

Then the "solution" is the point (10/3, 1/3).

Answer 2

A solution of a system of equations is a list of numbers x , y , z ,... that make all of the equations true simultaneously. The solution set of a system of equations is the collection of all solutions. Solving the system means finding all solutions with formulas involving some number of parameters.

Explanation:

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