Systems of Equations

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 occurs when the graphs of the equations intersect at exactly one point.

Front

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

Back

No solution occurs when the equations represent parallel lines, which 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 overlap completely.

Front

How do you solve a system of equations using the substitution method?

Back

To solve using substitution, solve one equation for one variable, then substitute that expression into the other equation.

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How do you solve a system of equations using the elimination method?

Back

To solve using 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 system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where the intersection points represent the solutions.

Front

What is the significance of the coefficients in a system of equations?

Back

Coefficients determine the slope and position of the lines in the graph, affecting the number of solutions.

Front

How can you determine if a system of equations is consistent or inconsistent?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Front

What is the role of the constant term in a linear equation?

Back

The constant term affects the y-intercept of the line in the graph, shifting it up or down.