Systems of Equations (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 systems of 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 = 2x + 3?

Back

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

Front

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

Back

Identify one equation and solve it for one variable.

Front

If x = 2, what is the value of y in the equation y = 3x - 1?

Back

y = 3(2) - 1 = 5.

Front

What is the solution to the system of equations: x + y = 10 and x = 4?

Back

Substituting x = 4 into the first equation gives y = 6, so the solution is (4, 6).

Front

What does it mean if two equations in a system have no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

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

Back

Substitute the solution back into both original equations to see if they hold true.

Front

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

Back

Set the equations equal: 2x + 1 = -x + 4. Solving gives x = 1, y = 3, so the solution is (1, 3).