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10-6 Systems of Equations

By: The Great and Honorable ME

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Vocabulary

System of equations: is a set of two or more

equations that contain two or more variables

Solution of a system of equations: is a set ofvalues that are solutions of all of the

equations.

If the system has two variables, the solutions

can be written as ordered pairs.

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Identifying Solutions of a system of

equations This is EASIER to do without the calculator.

EX. Determine if each ordered pair is a solution of the system ofequations below

2x + 3y = 8 and x 4y =15

A. ( -2, 4)

Plug in values to see if they are equal

2(-2) + 3(4) = 8

-4 + 12 = 8

8=8 (True)

(-2) 4(4) = 15 -2 16 = 15

-18 15 (Not True)

So (-2, 4) is not a solution

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Identifying Solutions of a system of

equations EX. Determine if each ordered pair is a solution of the

system of equations below

2x + 3y = 8 and x 4y =15

B. ( 7,-2)

Plug in values to see if they are equal

2(7) + 3(-2) = 8

14 + (-6) = 8

8=8 (True)

(7) 4(-2) = 15 7 (-8) = 15

15 = 15 (True)

So (7, -2) IS a solution

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Identifying Solutions of a system of

equations EX. Determine if each ordered pair is a solution of the

system of equations below

2x + 3y = 8 and x 4y =15

C. ( 11,-1)

Plug in values to see if they are equal

2(11) + 3(-1) = 8

22+ (-3) = 8

198 (Not True)

(11) 4(-1) = 15 11 (-4) = 15

15 = 15 (True)

So (11, -1) Is NOTa solution

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Solving systems of equations

Solve the system of equationsy = x + 3 and y = 2x + 5

The expression x + 3 and 2x + 5 both equal y, so they areequal to each other.

x + 3 = 2x + 5

Solve for x

x = -2

To find y, substitute 2 in for x in either equation.

y = x + 3 y = -2 + 3 y = 1.

The solution is (-2, 1)

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Solving systems of equations

CHECK your answers by plugging in(-2,1)

y = x + 3

(1) = (-2) + 3 1 = 1 ( True)

y = 2x + 5

(1) = 2(-2) + 5

1 = 1 ( True)

Answer checks out!!

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Solving systems of equations

Sometimes we have to put equation into y =

mx + b form first.

Ex. Solve the systems of equations forx + y = 5 and x 2y = -4

We get y = -x + 5 and y = x/2 + 2

Follow previous steps

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Solving systems of equations

Check

x + y = 5

(2) + (3) = 5 5 = 5 (True)

x 2y = -4

(2) 2(3) = -4

2 6 = -4

-4 = -4 (True)

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Solving systems of equations

Let our two numbers be x and y

x + y = 24

y = x 6

Plug both equations into calculator. y = -x + 24 and y = x 6

solve

(15, 9)

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1. Clear calculator

2. Make sure equations are in

y=mx + b form

3. y= button, enter equations4. Zoom button

5. 2nd key, Trace button.

6. #5 intersect

7. Enter, enter, enter

8. Intersect is .. ( ___, ___)

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