Systems of equations review

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 if a system of equations has no solution?

Back

It means 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

It means the equations represent the same line, so every point on the line is a solution.

Front

What is the substitution method for 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 the elimination method for 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

Solve for x and y: 2x + 3y = 12 and x - y = 1.

Back

(3, 2) is the solution.

Front

What is the y-intercept of the equation y = 2x + 3?

Back

The y-intercept is 3, which is the point where the line crosses the y-axis.

Front

What is the slope of the line represented by the equation 3x - 4y = 12?

Back

The slope is 3/4 after rearranging the equation to slope-intercept form (y = mx + b).

Front

How can you check 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, the point is a solution.