Solving Systems by Graphing

Front

What is the general form of a linear equation in two variables?

Back

The general form of a linear equation in two variables is Ax + By = C, where A, B, and C are constants.

Front

How do you solve for y in the equation 8x + 4y = 16?

Back

To solve for y, isolate y on one side: 4y = 16 - 8x, then divide by 4: y = -2x + 4.

Front

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

Back

When two lines intersect on a graph, it means that the system of equations has a unique solution at the point of intersection.

Front

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

Back

The solution is the point where the two lines intersect, which can be found by solving the equations simultaneously.

Front

How can you determine the solution of a system of equations by graphing?

Back

By graphing each equation on the same set of axes and identifying the point(s) where the lines intersect.

Front

What is the significance of the coordinates (4, 3) in the context of a system of equations?

Back

The coordinates (4, 3) represent a solution to a system of equations, indicating that x = 4 and y = 3 satisfy both equations.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

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

Back

If two lines are parallel, the system of equations has no solution because the lines never intersect.

Front

What is the graphical representation of the solution to a system of equations with infinitely many solutions?

Back

The graphical representation is two lines that coincide, meaning they lie on top of each other.