Solutions of Equations and Inequalities Notes 5.1 Solutions of Equations and Inequalities

1) Write the equation in slope-intercept form by solving for y. Equations 1) Write the equation in slope-intercept form by solving for y. 2) Graph the equation. 3) Determine the solution. For an equation, the solution is all of the points on the line.

-x + 2y = -2 +x +x 2y = x – 2 2 2 y = 𝟏 𝟐 x - 1 Is (4,1) a solution to this equation? YES Is (-2, 5) a solution to this equation? NO

1) Write the inequality in slope-intercept form by solving for y. Inequalities 1) Write the inequality in slope-intercept form by solving for y. 2) Graph the inequality. You must decide if the line is solid or dashed. Solid ≤, ≥ Dashed <, > 3) Shade above or below the line. Below ≤, < Above ≥, > 4) Determine the solution. For an inequality, the solution is all of the points in the shaded region.

x + 2y < 2 -x -x 2y < -x + 2 2 2 y < −𝟏 𝟐 x + 1 2 2 y < −𝟏 𝟐 x + 1 Is (4,-1) a solution to this equation? NO Is (-2, -5) a solution to this equation? YES

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-x + 2y = -2 x + 2y < 2 -4 + 2(1) = -2 4 + 2(-1) < 2 -4 + 2 = -2 When deciding if a point is a solution, another method is to substitute the point into the equation or inequality and solve. When using this method, if you get a true statement then the coordinate is a solution. If you get a false statement, then it is not a solution. -x + 2y = -2 x + 2y < 2 Is (4,1) a solution to this equation? Is (4,-1) a solution to this inequality? -4 + 2(1) = -2 4 + 2(-1) < 2 -4 + 2 = -2 4 + (-2) < 2 -2 = -2 2 < 2 False True (4,1) is a solution (4,-1) is not a solution