Solve Systems of Equations using 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 a method where one equation is solved for one variable, and that expression is substituted into another equation.

Front

How do you solve for y in the equation y = 3x + 2?

Back

To solve for y, simply substitute a value for x into the equation.

Front

What is the first step in solving a system of equations using substitution?

Back

Identify one equation to solve for one variable.

Front

If x = 5, what is the value of y in the equation y = 3x - 5?

Back

y = 3(5) - 5 = 15 - 5 = 10, so (5, 10) is a solution.

Front

What is the solution to the system of equations: x = 7 - 2y and 2x + y = 5?

Back

Substituting x into the second equation gives (1, 3) as the solution.

Front

How do you check if a solution (x, y) is correct for a system of equations?

Back

Substitute x and y back into both original equations to see if they hold true.

Front

What is the solution to the system of equations: y = 7x + 9 and 2y + 2x = -14?

Back

The solution is (-2, -5) after substituting y into the second equation.

Front

What does it mean if two lines represented by equations are parallel?

Back

If two lines are parallel, they have no solutions because they never intersect.

Front

What is the solution to the system of equations: 2y + x = -4 and y = -3?

Back

The solution is (2, -3) after substituting y into the first equation.