System 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 does substitution mean in the context of solving equations?

Back

Substitution is a method of solving a system of equations by 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 = 8x + 1?

Back

To solve for y, simply substitute a value for x into the equation. For example, if x = 1, then y = 8(1) + 1 = 9.

Front

What is the solution to the system y = 8x + 1 and y = 6x + 3?

Back

The solution is (1, 9). This is where the two lines intersect.

Front

How do you find the intersection of two lines represented by equations?

Back

To find the intersection, solve the equations simultaneously to find the values of x and y that satisfy both equations.

Front

What is the first step in using substitution to solve the system 2x + 8y = 20 and y = 2?

Back

The first step is to substitute y = 2 into the first equation: 2x + 8(2) = 20.

Front

What is the solution to the system y = 4x + 9 and y = 5x + 10?

Back

The solution is (-1, 5). This is where the two lines intersect.

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, it means they have no points of intersection and therefore no solution.

Front

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

Back

You can check your solution by substituting the values of x and y back into both original equations to see if they hold true.

Front

What is the solution to the system y = x + 5 and 4x + y = 20?

Back

The solution is (3, 8). This is where the two lines intersect.