System of Equations 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 substitution mean in the context of solving equations?

Back

Substitution is the process of replacing a variable in one equation with an equivalent expression from another equation.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable. 4. Substitute back to find the first variable.

Front

What is the solution to a system of equations?

Back

The point (x, y) where the graphs of the equations intersect, representing the values that satisfy all equations in the system.

Front

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

Back

y = 2(2) + 3 = 7.

Front

What is the first step in solving the system: y = x + 5 and 4x + y = 20?

Back

Substitute y from the first equation into the second equation.

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, and every point on that line is a solution.

Front

Solve the system by substitution: y = 3x + 1, 2x - y = 4.

Back

(2, 7).

Front

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

Back

(1, 3).