system of equations 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 the context of solving equations?

Back

Substitution is a method of solving a system of equations by solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you solve the system: y = 8x + 1 and y = 6x + 3?

Back

Set 8x + 1 = 6x + 3. Solve for x to find x = 1, then substitute back to find y = 9. The solution is (1, 9).

Front

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

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Front

How do you solve the system: y = 3 - x and 3y + x = 5?

Back

Substitute y = 3 - x into 3y + x = 5. This gives 3(3 - x) + x = 5. Solve to find x = 2, then y = 1. The solution is (2, 1).

Front

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

Back

Substituting x = 6 into y = 2(6) - 3 gives y = 9. The solution is (6, 9).

Front

How do you solve the system: 2y + x = -15 and x = 3y?

Back

Substitute x = 3y into 2y + 3y = -15. This gives 5y = -15, so y = -3. Then, x = 3(-3) = -9. The solution is (-9, -3).

Front

What is the solution to the system: x - 3y = -13 and 4x + 2y = 4?

Back

Solve x - 3y = -13 for x, then substitute into 4x + 2y = 4. This gives x = -1 and y = 4. The solution is (-1, 4).

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines represented by the equations on a coordinate plane.

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.