Solving Systems of Equations by substitution (easy)

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

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

Back

Solving by substitution involves solving one equation for one variable and then substituting that expression into the other equation.

Front

If y = 4, what is the value of y in the equation x = 3y + 5?

Back

Substituting y = 4 into x = 3(4) + 5 gives x = 12 + 5 = 17. So, the solution is (17, 4).

Front

How do you find the intersection of two lines represented by equations?

Back

To find the intersection, solve the equations simultaneously to find the values of the variables that satisfy both equations.

Front

What is the solution to the system: y = 3x + 9 and y = -6?

Back

Substituting -6 for y in the first equation gives -6 = 3x + 9. Solving for x gives x = -5, so the solution is (-5, -6).

Front

What does it mean if a system of equations has no solution?

Back

A system has no solution if the lines represented by the equations are parallel and never intersect.

Front

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

Back

A system has infinite solutions if the equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

Substitute the solution back into both original equations to see if both equations are satisfied.

Front

What is the first step in solving the system: 4x + 2y = -6 and y = -8?

Back

Substitute y = -8 into the first equation: 4x + 2(-8) = -6.

Front

What is the solution to the system: -2x - 2y = 16 and y = -8?

Back

Substituting y = -8 into -2x - 2(-8) = 16 gives -2x + 16 = 16, so x = 0. The solution is (0, -8).