System of Equation Substitution

Front

What is a system of equations?

Back

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

Front

What does substitution mean in the context of solving equations?

Back

Substitution is the process of replacing a variable with an equivalent expression to solve equations.

Front

How do you solve a system of equations by substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

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

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

Back

y = 2(4) + 3 = 11.

Front

What is the first step in solving the system: x + y = 10 and y = 2x?

Back

Substitute 2x for y in the first equation: x + 2x = 10.

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, so every point on the line is a solution.

Front

Solve the system: y = 3x + 1 and 2x - y = 4. What is the solution?

Back

(1, 4)

Front

What is the substitution method used for?

Back

To find the values of variables in a system of equations.