(18) Solving Systems of Equations by Substitution (8th)

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 substitution mean in 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 the system of equations: y = 2x + 1 and y = 4x - 1?

Back

Set the equations equal to each other: 2x + 1 = 4x - 1. Solve for x to find x = 1, then substitute back to find y = 3.

Front

What is the solution to the system of equations: y = x + 20 and y = 6x?

Back

Set the equations equal: x + 20 = 6x. Solve for x to find x = 4, then substitute back to find y = 24.

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 is the solution to the system of equations: x - y = 0 and 9x + y = 0?

Back

The solution is (0, 0).

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines on a coordinate plane.

Front

How do you check the solution of a system of equations?

Back

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

Front

What is the solution to the system of equations: 5x + 4y = -14 and y = -7x - 15?

Back

The solution is (-2, -1).

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution, meaning the lines intersect at one or more points.