RE-TAKE FLASHCARD SYSTEM OF EQUATIONS 2

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.

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What does it mean to solve a system of equations by elimination?

Back

Solving by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

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

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

Front

What is the elimination method in solving equations?

Back

The elimination method involves manipulating equations to eliminate one variable, allowing for the straightforward solving of the remaining variable.

Front

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

Back

Coefficients represent the relationship between variables in an equation. They determine the slope and position of the lines represented by the equations.

Front

How can you check the solution of a system of equations?

Back

Substitute the solution back into the original equations to verify that both equations hold true.

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What is the graphical interpretation of a system of equations?

Back

The graphical interpretation involves plotting the equations on a coordinate plane; the solution is where the lines intersect.

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

Back

If two lines are parallel, it means there is no solution to the system, as the lines never intersect.

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

Back

If two lines coincide, it means there are infinitely many solutions, as every point on the line is a solution to the system.

Front

How do you form a system of equations from a real-world scenario?

Back

Identify the quantities involved, assign variables, and create equations based on the relationships and totals described in the scenario.