Solving Systems of Linear Equations in Two Variables

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What does it mean for two lines to intersect in a system of linear equations?

Back

When two lines intersect, it means there is a unique solution to the system of equations, represented by the coordinates of the intersection point.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a linear equation in two variables?

Back

The graphical representation of a linear equation in two variables is a straight line on a coordinate plane.

Front

What is the elimination method for solving systems of linear equations?

Back

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

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

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

Back

If a system has infinitely many solutions, it means the equations represent the same line, and every point on that line is a solution.

Tags

CCSS.8.EE.C.8A

Front

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

Back

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

Tags

CCSS.8.EE.C.8A

Front

What is the substitution method for solving systems of linear equations?

Back

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

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

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

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

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

Back

To find the y-intercept, set x = 0 in the equation and solve for y.