Checking solutions to linear systems

Front

What is a linear system?

Back

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

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What does it mean for an ordered pair to be a solution to a linear system?

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An ordered pair is a solution to a linear system if it satisfies all equations in the system.

Front

How do you check if an ordered pair is a solution to a system of equations?

Back

Substitute the x and y values of the ordered pair into each equation. If both equations are true, it is a solution.

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What is the graphical representation of a linear system?

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

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What does it mean if a linear system has no solution?

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A linear system 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 linear system has infinitely many solutions?

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A linear system has infinitely many solutions if the equations represent the same line, meaning they overlap completely.

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What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

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The solution is (1, 3).

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What is the solution to the system of equations: 2x + 3y = 6 and 4x + 6y = 12?

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The system has infinitely many solutions because the second equation is a multiple of the first.

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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 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.