System of linear Equations

Front

What is a system of linear equations?

Back

A set of 2 or more equations that have the same variables.

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

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

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How do you solve a system of equations by substitution?

Back

You solve one equation for one variable and substitute that expression into the other equation.

Front

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

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The solution is the point(s) where the lines intersect on a graph.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

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How can you determine the number of solutions in a system of equations?

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By analyzing the slopes and y-intercepts of the lines: parallel lines (no solution), same line (infinitely many solutions), intersecting lines (one solution).

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What is the substitution method?

Back

A method for solving systems of equations by replacing one variable with an expression from another equation.

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What is the elimination method?

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A method for solving systems of equations by adding or subtracting equations to eliminate a variable.

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What is a consistent system of equations?

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A system that has at least one solution.