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 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 y = 4x + 6 and -5x - y = 21?

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The first step is to substitute the expression for y from the first equation into the second equation.

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What is the solution to the system of equations y = 3x - 8 and y = 4 - x?

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The solution is (3, 1), which means x = 3 and y = 1.

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What is the graphical interpretation of a solution to a system of equations?

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The graphical interpretation of a solution is the point where the graphs of the equations intersect.

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

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If a system of equations has no solution, it means that the equations represent parallel lines that never intersect.

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

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If a system of equations has infinitely many solutions, 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 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 in solving systems of equations?

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The substitution method involves solving one equation for one variable and substituting that value into the other equation.