Solving Linear Systems by Graphing

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What is a linear system?

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A linear system is a collection of two or more linear equations involving the same variables.

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What does it mean to solve a linear system by graphing?

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To solve a linear system by graphing means to plot the equations on a graph and identify the point(s) where they intersect, which represents the solution(s) to the system.

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What is the solution to a system of equations?

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The solution to a system of equations is the set of values for the variables that makes all equations true, often represented as an ordered pair (x, y).

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What does it mean if two lines are parallel in a linear system?

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If two lines are parallel, it means they have the same slope but different y-intercepts, indicating that there is no solution to the system.

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What does it mean if two lines coincide in a linear system?

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If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions to the system.

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How can you determine if a system of equations has no solution?

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A system has no solution if the lines are parallel, meaning they never intersect.

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What is the substitution method in solving linear systems?

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

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What is the elimination method in solving linear systems?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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How do you find the x-intercept of a linear equation?

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To find the x-intercept, set y = 0 in the equation and solve for x.

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How do you find the y-intercept of a linear equation?

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To find the y-intercept, set x = 0 in the equation and solve for y.