1. Solutions of Equations and Inequalities
Notes 5.1
Solutions of Equations and Inequalities

2. 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.

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

4. 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.

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

6. Put this information on the back of your note sheet!!!
above
below

7. -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
= -2
4 + (-2) < 2
-2 = -2
2 < 2
False
True
(4,1) is a solution
(4,-1) is not a solution