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## 2/1 - Systems of Equations **Systems of equations** are two or more linear equations that work together using the same variables, x and y, and are always grouped together. **System of equations $$\\begin{align} y = 3x + 2 \\\\ y = 4x - 6 \\end{align}$$ With systems of equations you can have up...

## 2/1 - Systems of Equations **Systems of equations** are two or more linear equations that work together using the same variables, x and y, and are always grouped together. **System of equations $$\\begin{align} y = 3x + 2 \\\\ y = 4x - 6 \\end{align}$$ With systems of equations you can have up to THREE possible outcomes. ### Solution * Equations share a common value/point. * Lines intersect at one point. ### No Solution * Equations don't share a common value/point * Lines are parallel ### Infinite Solutions * Equations share all values/points * Lines overlap on graph ## Graphing Systems ### Example $y = 2x + 0$ $y = 1x + 2$ A graph showing two lines intersecting at the point (2, 4). ### Solution * A solution means that you have found a value for x and y that work for BOTH equations. * When graphing the lines will intersect at the solution. * Equations will have different slopes. * A solution means that BOTH equations share the same x and y values at that point.