Solving System 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.

Front

How do you solve a system of equations graphically?

Back

To solve graphically, plot each equation on the same graph and identify the point(s) where they intersect.

Front

What does it mean for a point to be a solution to a system of equations?

Back

A point is a solution if it satisfies all equations in the system, meaning it makes all equations true.

Front

What is substitution method in solving systems of equations?

Back

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

Front

What is elimination method in 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.

Front

What is the graphical representation of the equation y = mx + b?

Back

This equation represents a straight line where 'm' is the slope and 'b' is the y-intercept.

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How can you determine if a system of equations has no solution?

Back

A system has no solution if the lines are parallel, meaning they never intersect.

Front

How can you determine if a system of equations has infinitely many solutions?

Back

A system has infinitely many solutions if the equations represent the same line, meaning they overlap completely.

Front

What is the first step in solving the system of equations 3x + 2y = 16 and 7x + y = 19?

Back

You can use either substitution or elimination. For elimination, you might multiply the second equation to align coefficients.

Front

What does it mean for two equations to be dependent?

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Two equations are dependent if they represent the same line, resulting in infinitely many solutions.