solving systems of equations by 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 solving equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into another equation.

Front

How do you solve for y in the equation y = -2x + 18?

Back

To solve for y, simply substitute the value of x into the equation.

Front

What is the first step in solving the system of equations by substitution?

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 = 8 and y = -2x + 18, how do you find x?

Back

Set the two equations equal to each other: 8 = -2x + 18, then solve for x.

Front

What is the solution to the system of equations y = 8 and y = -2x + 18?

Back

The solution is (5, 8).

Front

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

Back

Substitute the solution back into both original equations to see if both equations are satisfied.

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What is the solution to the system of equations 3x + y = 1 and y = 4x + 1?

Back

The solution is (0, 1).

Front

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

Back

Solve the equations simultaneously using substitution or elimination to find the point where they intersect.