Systems 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 systems of equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into another equation to find the values of the variables.

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 solving the system x - 2y = 1 and x + 4y = 7 using substitution?

Back

Solve one of the equations for x or y. For example, from x - 2y = 1, you can express x as x = 2y + 1.

Front

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

Back

The solution is (1, 2).

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

Back

It means that the equations represent parallel lines that never intersect, indicating that there are no values for the variables that satisfy all equations.

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What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines represented by the equations. Each intersection point corresponds to a solution of the system.

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

Back

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

Front

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

Back

Coefficients determine the slope and position of the lines represented by the equations. They affect the number of solutions the system may have.

Front

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

Back

The solution is approximately (1.4, -0.3).