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.

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

Back

Solving a system of equations using elimination involves adding or subtracting the equations to eliminate one variable, making it easier to solve for the remaining variable.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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 solution to the system: 3x - 5y = 8 and 2x + 5y = -3?

Back

(1, -1)

Front

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

Back

Substitute the solution values back into the original equations to see if they satisfy all equations.

Front

What is the graphical interpretation of a system of equations?

Back

The solution to a system of equations can be represented as the point(s) where the graphs of the equations intersect.

Front

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

Back

A system has no solution if the equations represent parallel lines that never intersect.

Front

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

Back

A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

Front

What is the first step in solving the system: y = 3 - x and 3y + x = 5?

Back

Substitute y = 3 - x into the second equation (3(3 - x) + x = 5).