Systems of equations review

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the graphs of the equations: if they intersect at one point, there is one solution; if they are parallel, there is no solution; if they overlap, there are infinitely many solutions.

Front

What is the graphical representation of the equation y = mx + b?

Back

It is a straight line where 'm' is the slope and 'b' is the y-intercept.

Front

What is the slope of the line represented by the equation 2x + 3y = 6?

Back

The slope is -2/3 after rearranging the equation to slope-intercept form (y = mx + b).

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

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

Front

What does the term 'consistent' mean in relation to systems of equations?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Front

What is the solution to the system of equations: x + y = 10 and x - y = 2?

Back

The solution is (6, 4).