Systems of Equations: Substitution

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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What does substitution mean in the context of solving equations?

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Substitution is a method of solving a system of equations by solving one equation for one variable and then substituting that expression into the other equation.

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To solve for y, simply substitute any value of x into the equation. For example, if x = 1, then y = 3 - 1 = 2.

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The solution is (2, 1).

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The solution is (4, 3).

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Substitute x = 6 into the equation: y = 2(6) - 3 = 12 - 3 = 9. So, y = 9.

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The solution is (6, 9).

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What does it mean if a system of equations has one solution?

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It means that the graphs of the equations intersect at exactly one point.

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What does it mean if a system of equations has no solution?

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It means that the graphs of the equations are parallel and never intersect.

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What does it mean if a system of equations has infinite solutions?

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It means that the equations represent the same line, and every point on the line is a solution.