Fundamental Mathematics/Arithmetic/Linear equation/Roots of System of Linear Equations

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Roots of System of Linear Equations [edit | edit source]

One was mentioned above, but there are other ways to solve a system of linear equations without graphing.

Variable Elimination[edit | edit source]

Multiply 1st row by 2 add to 2nd row

Yields

=>

Multiply 1st row by -3 add to 2nd row

Yields

=>

Substitution[edit | edit source]

If you get a system of equations that looks like this:

You can switch around some terms in the first to get this:

Then you can substitute that into the bottom one so that it looks like this:

Then, you can substitute 2 into an x from either equation and solve for y. It's usually easier to substitute it in the one that had the single y. In this case, after substituting 2 for x, you would find that y = 7.

Determinant[edit | edit source]

If you get a system of equations that looks like this:

Solve for y

Solve for x