Algebra I - Writing Systems of Equations

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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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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 represent the same scenario.

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CCSS.HSA.CED.A.3

Front

What does the variable 'x' typically represent in a system of equations?

Back

In a system of equations, 'x' usually represents one of the unknown quantities we are trying to solve for.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does the variable 'y' typically represent in a system of equations?

Back

In a system of equations, 'y' usually represents the other unknown quantity we are trying to solve for.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you solve a system of equations graphically?

Back

Graph each equation on the same coordinate plane. The point(s) where the lines intersect represent the solution(s) to the system.

Tags

CCSS.8.EE.C.8B

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method in solving systems of equations?

Back

The elimination method 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 does it mean if a system of equations has no solution?

Back

A system has no solution if the lines represented by the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

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.

Tags

CCSS.8.EE.C.8A

Front

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

Back

Substitute the values of the variables back into the original equations to see if they satisfy both equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6