Systems of Equations by 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 by 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 solution is the point (x, y) where the equations intersect, representing values that satisfy all equations in the system.

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 there are countless points of intersection.

Front

Solve by substitution: 5x + 4y = -14, y = -7x - 15

Back

(-2, -1)

Front

Solve by substitution: x = -3y - 17, 2x + 3y = -7

Back

(10, -9)

Front

Solve by substitution: y = 8x + 1, y = 6x + 3

Back

(1, 9)

Front

Solve by substitution: y = -6x + 5, -2x + y = 5

Back

(0, 5)