Solve Systems of Equations using Substitution

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 for y in the equation y = -1x - 5?

Back

To solve for y, simply substitute any value of x into the equation. For example, if x = 0, then y = -5.

Front

What is the first step in solving the system: y = -1x - 5 and 4x - 8y = 4?

Back

The first step is to substitute the expression for y from the first equation into the second equation.

Front

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

Back

The solution is (-2, -5).

Front

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

Back

To check a solution, substitute the values of the solution into both equations. If both equations are true, the solution is correct.

Front

What does it mean if two lines intersect at a point?

Back

If two lines intersect at a point, it means that there is a unique solution to the system of equations represented by those lines.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection of the lines on a coordinate plane, where each line represents one equation.

Front

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

Back

The solution is (2, -3).

Front

What is the purpose of solving systems of equations?

Back

The purpose is to find the values of the variables that satisfy all equations in the system simultaneously.