Systems 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 is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you solve for y in the equation y = -2x?

Back

To solve for y, simply substitute any value of x into the equation. For example, if x = 1, then y = -2(1) = -2.

Front

Given the equations y = -2x and 4x - y = 0, what is the solution using substitution?

Back

Substituting y = -2x into 4x - y = 0 gives 4x - (-2x) = 0, which simplifies to 6x = 0, so x = 0. Then, y = -2(0) = 0. The solution is (0,0).

Front

How do you find the value of x in the equation x = 3y?

Back

To find x, substitute any value of y into the equation. For example, if y = -3, then x = 3(-3) = -9.

Front

What is the solution to the system of equations 2y + x = -15 and x = 3y?

Back

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

Front

What does it mean if a system of equations has no solutions?

Back

A system has no solutions if the lines represented by the equations are parallel and never intersect.

Front

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

Back

A system has infinite solutions if the equations represent the same line, meaning every point on the line is a solution.

Front

How do you solve the system 5x + 3y = 7 and y = 4 using substitution?

Back

Substituting y = 4 into 5x + 3(4) = 7 gives 5x + 12 = 7, so 5x = -5, thus x = -1. The solution is (-1, 4).

Front

What is the first step in using the substitution method?

Back

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