Solving Systems of Equations with Substitution 2

Solving Systems of Equations with Substitution (Day 2)

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Multiple Choice

What is a system of equations?

• a set of equations

• a calculator

• one equation that can be solved by a system of steps

• a equation that can not be solved.

~REMEMBER~

A system of equations is a set of equations.

When solving we can have no solution, one solution, or an infinite number of solutions.

If there is one solution the solution is a coordinate with a x and y value.

(X, Y)

Multiple Choice

Given the system

y = 2x + 1

3x + y = -9

What should be substitute into the second equation for y?

WARNING - You need to write this down!

• 3x + y

• x

• -9

• 2x + 1

Multiple Choice

After substituting the expression in our new equation is____________.

• 3x + 2x + 1 = -9

• 2x + 3 = -9

• 3x + x = -9

• None of these.

So the equation is.....

3x + 2x + 1 = -9

Multiple Choice

What is the value of x?

• x = 4

• x = -2

• x = -3

• x = -4

How did we get x?

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Multiple Choice

Are you done?

Multiple Choice

Please solve for y.

Hint - You substitute your value for x in either equation to find y.

• y = -3

• y = 3

• y = 2

• y = -2

How did we get y?

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Multiple Choice

Then the solution to the system is..........

• (-3,-2)

• y = -3

• (-2,-3)

• There is no solution the lines are parallel.

Poll

So what do you think?

• I am totally lost

• I am starting to get it

• feeling good

• piece of cake!

Multiple Choice

Please try this one!

y = x - 8

y = 5x

• I have an answer!

• I am stuck....

• Not sure where to start

Did you get a solution of (-2, -10)? How?

y = x - 8

y = 5x

• Substitute 5x for y: 5x = x - 8

• Subtract x from both sides: 4x = -8

• Divide both sides by 4: x = -2

• Find y by substituting -2 in for x: y = 5(-2)

• y = -10

• Therefor the solution is (-2,-10)

Multiple Choice

Lets try another!

y = x + 11

y = 12x

• (1, 12)

• (12, 1)

• (-12, -1)

• (-1, -12)

Multiple Choice

y = 2x -3

x + y = 18

• (10,8)

• (7,11)

• (19, -1)

• (0, 18)

Multiple Choice

Last One!

x + 14y = 84

2x - 7y = -7

• (3, -7)

• (5, 14)

• (14, 5)

• (-7, 3)