Solving Systems of Equations with 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 the system of equations 5x - 2y = 3 and y = 2x using substitution?

Back

1. Substitute y in the first equation: 5x - 2(2x) = 3. 2. Solve for x: 5x - 4x = 3 -> x = 3. 3. Substitute x back to find y: y = 2(3) = 6. Solution: (3, 6).

Front

What is the first step in solving x = 6 and y = 2x - 3 using substitution?

Back

Since x is already isolated, substitute x = 6 into the second equation: y = 2(6) - 3.

Front

What is the solution to the system of equations x = 6 and y = 2x - 3?

Back

The solution is (6, 9).

Front

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

Back

It means that the equations represent the same line, and there are countless points that satisfy both equations.

Front

How do you determine if a system of equations has no solution?

Back

If the lines represented by the equations are parallel, they will never intersect, indicating no solution.

Front

Solve the system of equations y = 3 - x and 3y + x = 5 using substitution.

Back

1. Substitute y in the second equation: 3(3 - x) + x = 5. 2. Solve for x: 9 - 3x + x = 5 -> -2x = -4 -> x = 2. 3. Substitute x back to find y: y = 3 - 2 = 1. Solution: (2, 1).

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines on a coordinate plane, which represent the solutions.

Front

What is the importance of checking your solution in a system of equations?

Back

Checking ensures that the solution satisfies all equations in the system, confirming its accuracy.