### Systems of linear equations: An equation of a line

### A linear equation with two unknowns

Linear equation with two unknowns

A An equation is true when you substitute the value of #\blue x# and #\green y# of that point in the equation, and the left and right hand side of the equation are equal. |
\[3\cdot \blue{x}+5 \cdot \green{y}+5=0 \] The point #\rv{\blue 0,-\green{1}}# is a solution: \[3\cdot \blue{0}+5 \cdot \green{-1}+5=0\] |

Yes

After all, to determine if the point #\rv{2, {{16}\over{3}}}# is a solution to the equation, we enter the point in the equation. If the equation is true, then the point is a solution. If the equation is not true, then the point is not a solution to the equation. In this case we have:

\[-5\cdot 2+3\cdot {{16}\over{3}}-6=0\]

The equation is true, hence # \rv{2, {{16}\over{3}}}# is a solution to the equation.

After all, to determine if the point #\rv{2, {{16}\over{3}}}# is a solution to the equation, we enter the point in the equation. If the equation is true, then the point is a solution. If the equation is not true, then the point is not a solution to the equation. In this case we have:

\[-5\cdot 2+3\cdot {{16}\over{3}}-6=0\]

The equation is true, hence # \rv{2, {{16}\over{3}}}# is a solution to the equation.

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