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 set of values that satisfy all equations simultaneously.

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 a system of equations using substitution?

Back

1. Solve one of the equations for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable. 4. Substitute back to find the other variable.

Front

What is the first step in using substitution to solve the system: 2y + x = -15 and x = 3y?

Back

The first step is to substitute the expression for x from the second equation (x = 3y) into the first equation (2y + x = -15).

Front

What is the solution to the system of equations 2y + x = -15 and x = 3y?

Back

The solution is (-9, -3).

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What is the solution to the system of equations -3x - 3y = 3 and y = -5x - 17?

Back

The solution is (-4, 3).

Front

How do you determine if a point is a solution to a system of equations?

Back

To determine if a point is a solution, substitute the x and y values of the point into each equation. If both equations are satisfied, the point is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the intersection of the lines represented by each equation on a coordinate plane.

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

Back

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

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

Back

If two lines coincide, it means they are the same line, and the system has infinitely many solutions.