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Wednesday 24th of May
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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solutions to Linear Equations in Two Variables

In this section we will learn to use that same technique to determine if given values as points (x, y) make a true statements of linear equations in two variables. These points are called solutions or truth values. We will also build tables as sequences of truth values.

EXAMPLES:

1. Given 2x − 3y = 6 use the replacement values for the points (x, y) to see if the points lie on the line defined by the equation. [That is, see if the points make a true statement of the equation.]

Do the points (3, 0), (-3, -3) , (0, -2), (6, 2) satisfy the equation?

Use the points as replacements:

 2(3) − 3(0) = 6 ?? 6 − 0 = 6 This point is on the line. 2(-3) − 3(-3) = 6 ?? -6 − (-9) ≠ 6 This point is not on the line. 2(0) − 3(-2) = 6 ?? 0 − (-6) = 6 This point is on the line. 2(6) − 3(2) = 6 ?? 12 − 6 = 6 This point is on the line.

2. Given 5x + 2y = 10 use the replacement values for the points (x, y) to see if the points lie on the line defined by the equation. [That is, see if the points make a true statement of the equation.]

Do the points (2, 0), (-2, 10), (4, -2) (0, 5) satisfy the equation?

Use the points as replacements:

 5(2) + 2(0) = 10 ?? 10 + 0 = 10 This point is on the line. 5(-2) + 2(10) = 10 ?? -10 + 20 = 10 This point is on the line. 5(4) + 2(-2) = 10 ?? 20 + (- 4) ≠ 10 This point is not on the line. 5(0) + 2(5) = 10 ?? 0 + 10 = 10 This point is on the line.

NOTE: This method can be used to check your points and solutions to applications.