When does an inequality sign flip direction? Where do two lines meet?
Solving an inequality works almost exactly like solving an equation, except the direction flips when you multiply or divide by a negative number. For a system of equations, graph each equation as a line, and the point where they meet is the solution.
An equation finds "exactly what value," while an inequality finds "which range." The method for solving them is almost the same, except for one thing — multiply or divide both sides by a negative number, and the inequality sign flips direction. Multiply both sides of 2<5 by −1 and you get −2>−5, which shows why the direction has to flip.
A system of equations is a problem where you find the values that satisfy two equations with two unknowns at the same time. Graph each equation as a line, and the single point where the two lines meet is the answer.
Solve an inequality step by step and check whether the direction really does flip when you divide by a negative number, and for the system of equations, graph both lines and try to guess the intersection point yourself.
Properties of inequalities: adding or subtracting the same number on both sides keeps the direction the same. Multiplying or dividing both sides by a positive number also keeps the direction the same, but multiplying or dividing both sides by a negative number flips the direction.
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A system of equations means finding the x and y that satisfy two equations at once. Graph each equation as a line, and the coordinates of the point where the two lines meet is the answer.
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The intersection point of the two lines is the single point that satisfies both equations at once. That's exactly the solution to the system.