Solving Systems of Equations: Graphing, Substitution, and Elimination

The video tutorial covers methods for solving systems of equations, including graphing, substitution, and elimination. It explains how to graph equations by hand or using tools, solve equations for variables, and find solutions where lines intersect. The tutorial also addresses solving 3x3 systems, applying these methods to real-world problems, and understanding inconsistent and infinite solutions.

What is the first step in graphing systems of equations by hand?

• Convert equations to slope-intercept form

• Choose a suitable scale for the graph

• Draw the axes and plot points

• Identify the type of graph to use

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CCSS.8.EE.C.8B

What does the 'b' in the slope-intercept form represent?

• The coefficient of x

• The y-intercept of the graph

• The x-intercept of the graph

• The slope of the line

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CCSS.8.EE.B.6

CCSS.8.F.A.3

How do you find the solution to a system of equations graphed on a coordinate plane?

• The origin point of the graph

• The highest point on the graph

• The point where the lines intersect

• The point where the y-values are equal

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CCSS.8.EE.C.8B

In substitution, what is the next step after solving one equation for a variable?

• Substitute the expression into the other equation

• Check the solution by plugging back the values

• Graph the equations to find the intersection

• Solve for the second variable directly

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What is the result of substituting '11 + 2y' for 'x' in another equation?

• None of the above

• Simplifies the equation to one variable

• Eliminates the variable y from the equation

• Creates a new equation with two variables

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What is the purpose of making coefficients equal in the elimination method?

• To prepare the equations for graphing

• To find the value of one variable directly

• To eliminate one variable by adding the equations

• To simplify the equations

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What happens when you add two equations in the elimination method?

• One variable is eliminated

• A new equation is formed

• All of the above

• The equations become simpler

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What indicates that a system of equations is inconsistent?

• The equations represent the same line

• The system has infinitely many solutions

• The system has no solutions

• The system has one solution

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CCSS.8.EE.C.8B

At what point do the costs of two companies become equal according to the graph?

• After 1 hour

• After 2 hours

• They never become equal

• After 3 hours

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CCSS.8.EE.C.8C

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

• The lines intersect at multiple points

• The lines are parallel

• The lines never intersect

• The lines are coincident

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CCSS.8.EE.C.8A