Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation to find the values of both variables.

Front

How do you solve for y in the equation x = -3y - 17?

Back

To solve for y, rearrange the equation: y = (-x - 17)/3.

Front

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

Back

It means that the equations represent the same line, and thus every point on that line is a solution to the system.

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.

Front

How can you check if your solution to a system of equations is correct?

Back

You can check by substituting the values of the variables back into the original equations to see if they hold true.

Front

What is the solution to the system of equations 2x + 3y = -7 and x = -3y - 17?

Back

The solution is (10, -9).

Front

What is the significance of the coefficients in a system of linear equations?

Back

The coefficients determine the slope and position of the lines represented by the equations, affecting whether they intersect at one point, are parallel, or are the same line.

Front

What is the graphical interpretation of a system of equations with one solution?

Back

It means that the lines representing the equations intersect at exactly one point.

Front

How do you isolate a variable in an equation?

Back

You perform algebraic operations to get the variable on one side of the equation and all other terms on the opposite side.

Front

What is the solution to the system of equations 4x - 5y = 21 and x - 3y = 7?

Back

The solution is (4, -1).