Solving Systems of Equations

Front

What is the solution to a system of equations?

Back

The solution (x, y) is the point where the equations intersect.

Tags

CCSS.8.EE.C.8B

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.

Tags

CCSS.8.EE.C.8A

Front

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

Back

By analyzing the slopes and y-intercepts of the equations; if they are the same, there are infinitely many solutions; if different, one solution; if parallel, no solution.

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method in solving systems of equations?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphing method for solving systems of equations?

Back

It involves plotting both equations on a graph and identifying the point of intersection.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for two lines to be coincident?

Back

It means they lie on top of each other, representing infinitely many solutions.

Tags

CCSS.8.EE.C.8A

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it moves; a positive slope rises, while a negative slope falls.

Tags

CCSS.8.EE.B.5

Front

How do you find the x-intercept of a linear equation?

Back

Set y to 0 and solve for x.

Front

How do you find the y-intercept of a linear equation?

Back

Set x to 0 and solve for y.