Solving Systems by Substitution

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What is a system of linear equations?

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A system of linear equations is a set of two or more linear 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 by substitution?

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

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It means that the equations represent the same line, and there are an infinite number of points that satisfy both equations.

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

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It means that the equations represent parallel lines that never intersect.

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

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Substitute the solution back into the original equations to see if both equations are satisfied.

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What is the graphical representation of a system of linear equations?

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The graphical representation is the intersection point(s) of the lines represented by the equations.

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What is the significance of the slope in a linear equation?

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The slope indicates the steepness of the line and the direction it goes (positive or negative).