Solve the systems of linear equations by substitution and highlight or circle the answer as an "ordered pair".

9.) y= -6x + 10
y= 3x + 1

Eliminate the equal sides of each equation and combine.

−

6

x

+

10

=

3

x

+

1

-

6

x

+

10

=

3

x

+

1

Move all terms containing

x

x

to the left side of the equation.

Subtract

3

x

3

x

from both sides of the equation.

−

6

x

+

10

−

3

x

=

1

-

6

x

+

10

-

3

x

=

1

y

=

3

x

+

1

y

=

3

x

+

1

Subtract

3

x

3

x

from

−

6

x

-

6

x

.

−

9

x

+

10

=

1

-

9

x

+

10

=

1

y

=

3

x

+

1

y

=

3

x

+

1

Move all terms not containing

x

x

to the right side of the equation.

Subtract

10

10

from both sides of the equation.−

9

x

=

1

−

10

-

9

x

=

1

-

10

y

=

3

x

+

1

y

=

3

x

+

1

Subtract

10

10

from

1

1

.

−

9

x

=

−

9

-

9

x

=

-

9

y

=

3

x

+

1

y

=

3

x

+

1

Divide each term by

−

9

-

9

and simplify.

Divide each term in

−

9

x

=

−

9

-

9

x

=

-

9

by

−

9

-

9

.

−

9

x

−

9

=

−

9

−

9

-

9

x

-

9

=

-

9

-

9

y

=

3

x

+

1

y

=

3

x

+

1

Reduce the expression by cancelling the common factors

x =

−

9

−

9

x

=

-

9

-

9

y

=

3

x

+

1

y

=

3

x

+

1

Divide

−

9

-

9

by

−

9

-

9

.

x

=

1

x

=

1

y

=

3

x

+

1Replace all occurrences of

x

x

with the solution found by solving the last equation for

x

x

. In this case, the value substituted is

1

1

.

x

=

1

x

=

1

y

=

3

(

1

)

+

1

y

=

3

(

1

)

+

1

Simplify

3

(

1

)

+

1

3

(

1

)

+

1

.

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Multiply

3

3

by

1

1

.

x

=

1

x

=

1

y

=

3

+

1

y

=

3

+

1

Add

3

3

and

1

1

.

x

=

1

x

=

1

y

=

4

y

=

4

The solution to the system of equations can be represented as a point.

(

1

,

4

)

(

1

,

4

)

The result can be shown in multiple forms.

Point Form:

(

1

,

4

)

(

1

,

4

)

Equation Form:

x

=

1

,

y

=

4

part a

x     y

0     8

1     7.5

2     7

3     6.5

4     6

5     5.5  

for every hour i deducted .5 inches from the length of the candle

part b

it is a function because for every x value there is only one y value

part   c

for every x value there is only one y value

x       y

0       8

1       7.6

2       7.2

3       6.8

step-by-step explanation: