CA1 Solving Linear Systems Review

Front

What is a system of linear equations?

Back

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 on a graph.

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What does it mean for a system of equations to have a unique solution?

Back

A unique solution occurs when the lines represented by the equations intersect at exactly one point.

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What does it mean for a system of equations to have no solution?

Back

No solution occurs when the lines represented by the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

Infinitely many solutions occur when the equations represent the same line, meaning they intersect at every point on that line.

Front

How do you determine if a point is a solution to a system of equations?

Back

To determine if a point is a solution, substitute the x and y values of the point into each equation. If both equations are satisfied, the point is a solution.

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Back

The equation represents a straight line on a graph, where m is the slope and b is the y-intercept.

Front

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

Back

Front

How do you find the intersection of two lines graphically?

Back

To find the intersection graphically, plot both lines on the same graph and identify the point where they cross.

Front

What is the substitution method for solving systems of equations?

Back

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

Front

What is the elimination method for solving systems of equations?

Back

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