Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the graphical representation of a system of equations?

Back

The intersection point(s) of the lines represented by the equations on a coordinate plane.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What does it mean if a system of equations has no solution?

Back

The lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

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

Substitute the point's coordinates into each equation; if both equations are true, the point is a solution.

Front

What is the first step in solving the system: 7x + 4y = 12 and x + 2y = -4?

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

Front

Solve the system: x - 4y = 16 and 5x + 4y = 8.

Back

The solution is (4, -3).