Solving systems of equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for two equations to intersect on a graph?

Back

It means they have a common solution, which is the point where the two lines meet.

Front

How can you determine if a point is a solution to a system of equations?

Back

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

Front

What is the graphical representation of a solution to a system of equations?

Back

The point (x, y) where the lines of the equations intersect.

Front

What is the solution to the system of equations: y = 2x + 1 and y = 4x - 1?

Back

(1, 3)

Front

What does it mean if two lines are parallel in a system of equations?

Back

They have no solutions because they never intersect.

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

Front

What is the solution to the system of equations: 5x + 3y = 7 and y = 4?

Back

(-1, 4)

Front

Is (1, 10) a solution to the system: y = 7x + 5 and y = x + 9?

Back

No