Solving Systems by 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 to the system is the set of values that satisfy all equations simultaneously.

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What does it mean to solve a system of equations by substitution?

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Solving a system of equations by substitution involves solving one of the equations for one variable and then substituting that expression into the other equation.

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How do you isolate a variable in an equation?

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To isolate a variable, you perform algebraic operations to get the variable on one side of the equation and all other terms on the opposite side.

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What is the first step in solving the system of equations x + 2y = 8 and 3x - y = 5 by substitution?

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The first step is to solve one of the equations for one variable. For example, you can solve the first equation for x: x = 8 - 2y.

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What is the solution to the system of equations x + 2y = 8 and 3x - y = 5?

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The solution is (2, 3), meaning x = 2 and y = 3.

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What is the graphical representation of a system of equations?

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The graphical representation of a system of equations is the point(s) where the graphs of the equations intersect. Each intersection point represents a solution to the system.

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What does it mean if two lines are parallel in the context of a system of equations?

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If two lines are parallel, it means that the system of equations has no solution, as the lines never intersect.

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What does it mean if two lines coincide in the context of a system of equations?

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If two lines coincide, it means that the system of equations has infinitely many solutions, as every point on the line is a solution.

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How can you check if your solution to a system of equations is correct?

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You can check your solution by substituting the values back into the original equations to see if they hold true.

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What is the substitution method used for?

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The substitution method is used to solve systems of equations, particularly when one equation can be easily solved for one variable.