Substitution Method

Front

What is the substitution method in solving systems of equations?

Back

The substitution method is a technique used to solve systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

How do you solve for y in the equation y = 3x + 14?

Back

To solve for y, simply substitute a value for x into the equation. For example, if x = -2, then y = 3(-2) + 14 = 8.

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

Given the equations y = -4x and y = 3x + 14, how do you find the value of x?

Back

Set the two equations equal to each other: -4x = 3x + 14. Solve for x to find x = -2.

Front

What is the solution to the system of equations -4x + 4y = 8 and y = -2x - 10?

Back

The solution is (-4, -2).

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution back into both original equations. If both equations are satisfied, the solution is correct.

Front

What does it mean if two lines intersect at a point when solving a system of equations?

Back

It means that there is a unique solution to the system, which is the point of intersection.

Front

What is the solution to the system of equations y = x - 6 and y = -3x + 2?

Back

The solution is (2, -4).

Front

How do you solve the system y = 5x - 7 and -3x - 2y = -12 using substitution?

Back

Substitute y = 5x - 7 into -3x - 2y = -12, then solve for x and subsequently for y.

Front

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

Back

The solution is (1.4, -0.3).