Solving Systems of Equations 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 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 equation 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 a system of equations by substitution?

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The first step is to solve one of the equations for one variable in terms of the other variable.

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What is the solution to the system of equations y = -3x + 11 and y = -6x - 13?

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The solution is (-8, 35).

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

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

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What is the graphical interpretation of a system of equations?

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The graphical interpretation of a system of equations is the point(s) where the graphs of the equations intersect, representing the solution(s) to the system.

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What does it mean if two equations in a system have no solution?

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If two equations have no solution, it means their graphs are parallel and they never intersect.

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What does it mean if two equations in a system have infinitely many solutions?

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If two equations have infinitely many solutions, it means they represent the same line, and every point on that line is a solution.

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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 by replacing one variable with an expression derived from another equation.