One-two variables Equations Flashcard

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 to the system is the set of values that satisfy all equations simultaneously.

Front

How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions described in the problem into equations, and ensure the equations reflect the same variables.

Front

What does the solution (1, 3) represent in the context of a system of equations?

Back

The solution (1, 3) indicates that the value of the first variable is 1 and the value of the second variable is 3, which satisfies all equations in the system.

Front

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

Back

Coefficients represent the relationship between the variables in the equations. They indicate how much of each variable is involved in the equation.

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How can you determine if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines, meaning they have the same slope but different y-intercepts.

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What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, and any point on that line is a solution to the system.

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What is the graphical method for solving a system of equations?

Back

The graphical method involves plotting the equations on a coordinate plane and identifying the point(s) where the lines intersect, which represent the solution(s) to the system.

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What is the substitution method for solving a system of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to find the values of both variables.

Front

What is the elimination method for solving a system of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

Front

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

Back

Substitute the values of the solution into each equation of the system. If the left-hand side equals the right-hand side for all equations, the solution is correct.