Systems of Equations: Substitution/Graphing

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

What does it mean to solve a system of equations by substitution?

Back

Solving by substitution involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the first step in solving the system x - y = 11 and 2x + y = 19 using substitution?

Back

Solve the first equation for x: x = y + 11.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s) of the system.

Front

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

Back

If two lines are parallel, it means they have no solutions, as they never intersect.

Front

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

Back

If two lines coincide, they are the same line, indicating that there are infinitely many solutions.

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines: if slopes are equal and intercepts are different, no solution; if slopes are equal and intercepts are the same, infinitely many solutions; if slopes are different, one solution.

Front

What is the substitution method?

Back

The substitution method involves isolating one variable in one equation and substituting that expression into the other equation to solve for the remaining variable.

Front

What is the solution to the system 3x + 2y = 16 and 7x + y = 19?

Back

The solution is (1, -1).

Front

What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the values of the variables that satisfy all equations in the system.