Substitution (already isolated)

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

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 = 3, then y = 2(3) = 6.

Front

What is the first step in solving the system of equations x = 6 and y = 2x - 3?

Back

Substitute x = 6 into the second equation: y = 2(6) - 3.

Front

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

Back

Substituting y = 2x into 5x - 2(2x) = 3 gives x = 3, and substituting back gives y = 6. So the solution is (3, 6).

Front

Convert the equation 4x + 2y = 10 to slope-intercept form (y = mx + b).

Back

Rearranging gives y = -2x + 5.

Front

What does the slope-intercept form of a line represent?

Back

It represents a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope from the equation y = -2x + 5?

Back

The slope (m) is -2.

Front

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

Back

Substituting y = 3 - x into 3(3 - x) + x = 5 gives the solution (2, 1).

Front

What is the solution to the system 2x + 3y = 4 and y = 5x - 27?

Back

Substituting y = 5x - 27 into 2x + 3(5x - 27) = 4 gives the solution (5, -2).

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables.