Solving Systems using 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 it mean to solve a system of equations using substitution?

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

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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 isolate one variable in one of the equations.

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

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To check if a solution is correct, substitute the values of the solution into both equations to see if they hold true.

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

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A system of equations has no solution if the lines represented by the equations are parallel and never intersect.

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

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A system of equations has infinitely many solutions if the equations represent the same line, meaning they intersect at every point on that line.

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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 intersection point(s) of the lines represented by the equations.

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What is the solution to the system of equations y = 2x + 3 and y = -x + 1?

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The solution is (1, 5).

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How can you identify a system of equations that has exactly one solution?

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A system of equations has exactly one solution if the lines intersect at a single point, meaning they have different slopes.

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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 to find the other variable.