Solve Systems by Substitution

Front

What is a system of equations?

Back

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

Front

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

Back

It means to solve one equation for one variable and then substitute that expression into the other equation.

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Front

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

Back

It indicates that the system has no solution, as the lines never intersect.

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 first step in solving a system of equations by substitution?

Back

Isolate one variable in one of the equations.

Front

If y = 2x + 3, what is y when x = 4?

Back

y = 2(4) + 3 = 8 + 3 = 11.

Front

What is the graphical representation of the equation y = -3x + 11?

Back

A straight line with a slope of -3 and a y-intercept of 11.

Front

How can you check if your solution to a system of equations is correct?

Back

Substitute the solution back into both original equations to see if they hold true.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

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