Solving Systems of Two Linear Equations

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.

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

Back

A system has a unique solution when the graphs of 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

A system has no solution when the graphs of the equations are parallel and never intersect.

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

Back

A system has infinitely many solutions when the equations represent the same line, meaning they coincide.

Front

How do you solve a system of equations using substitution?

Back

To solve by substitution, solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

To solve by elimination, add or subtract the equations to eliminate one variable, making it easier to solve for the other.

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.

Front

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

Back

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

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What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it goes (positive slope rises, negative slope falls).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form.