Solving Systems of Equations with 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 set of values that satisfy all equations simultaneously.

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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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How do you solve a system of equations using substitution?

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1. Solve one of the equations for one variable. 2. Substitute that expression into the other equation. 3. Solve the resulting equation for the remaining variable. 4. Substitute back to find the other variable.

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What is the solution to the system of equations x = 6 and y = 2x - 3?

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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 that line is a solution.

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How can you determine the number of solutions in a system of equations?

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By analyzing the graphs of the equations: if they intersect at one point, there is one solution; if they are parallel, there is no solution; if they are the same line, there are infinite solutions.

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What is the graphical representation of a system of equations?

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The graphical representation consists of the lines or curves of the equations plotted on a coordinate plane.

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What is the first step in using substitution to solve a system of equations?

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Choose one of the equations and solve it for one variable.