Substitution

Front

What is substitution in solving systems of equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into another equation to find the values of the variables.

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 (x, y) that satisfy both equations.

Front

How do you solve for y in the equation y = 2x - 4?

Back

To solve for y, simply substitute any value of x into the equation. For example, if x = 3, then y = 2(3) - 4 = 2.

Front

What is the solution to the system of equations y = 2x + 3 and y = 5x?

Back

To find the solution, set 2x + 3 = 5x. Solving gives x = 1, and substituting back gives y = 5. So, the solution is (1, 5).

Front

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

Back

It means that the equations represent parallel lines that never intersect, indicating there are no common points (x, y) that satisfy both equations.

Front

How do you find the x-value when given y = 2x + 9 and x = -3?

Back

Substituting x = -3 into the equation gives y = 2(-3) + 9 = 3. So, the point is (-3, 3).

Front

What is the first step in solving the system of equations 4y = x and x = 5y + 2?

Back

The first step is to express x in terms of y using the first equation: x = 4y, and then substitute this into the second equation.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s) to the system.

Front

How can you verify the solution of a system of equations?

Back

You can verify the solution by substituting the values back into the original equations to see if both equations are satisfied.

Front

What is the significance of the slope in the equation y = mx + b?

Back

The slope (m) indicates the steepness of the line and the direction it goes; a positive slope rises, while a negative slope falls.