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Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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

Back

A unique solution means that there is exactly one point (x, y) that satisfies all equations in the system.

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

Back

No solution means that the equations represent parallel lines that 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 every point on the line is a solution.

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 into each equation. If both equations are true, the point is a solution.

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane.

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What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x).

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What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How can you find the intersection point of two lines graphically?

Back

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

Front

What is the substitution method in solving systems of equations?

Back

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