Systems of Equations: Graphing and Substitution

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 graph a system of equations?

Back

To plot the equations on a coordinate plane and find the point(s) where they 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

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

One solution: lines intersect at one point; no solution: lines are parallel; infinitely many solutions: lines are the same.

Front

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

Back

(1, 3)

Front

How do you solve the system of equations using the graphing method?

Back

Graph both equations on the same coordinate plane and identify the intersection point.

Front

What is the graphical representation of the equation y = 3x - 2?

Back

A straight line with a slope of 3 and a y-intercept of -2.

Front

What does the y-intercept represent in a linear equation?

Back

The point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

What is the slope of the line represented by the equation y = 4x - 10?

Back

4, indicating the line rises 4 units for every 1 unit it moves to the right.

Front

How do you find the x-value when given a y-value in a linear equation?

Back

Substitute the y-value into the equation and solve for x.