Which is the solution to the system of equations? y=1/3x+2 y=4/3x-5

x = 7 . y = 13/3

Step-by-step explanation:

Solve the following system:

{y = x/3 + 2

y = (4 x)/3 - 5

Express the system in standard form:

{-x/3 + y = 2

-(4 x)/3 + y = -5

Express the system in matrix form:

(-1/3 | 1

-4/3 | 1)(x

y) = (2

-5)

Write the system in augmented matrix form and use Gaussian elimination:

(-1/3 | 1 | 2

-4/3 | 1 | -5)

Swap row 1 with row 2:

(-4/3 | 1 | -5

-1/3 | 1 | 2)

Subtract 1/4 × (row 1) from row 2:

(-4/3 | 1 | -5

0 | 3/4 | 13/4)

Multiply row 1 by 3:

(-4 | 3 | -15

0 | 3/4 | 13/4)

Multiply row 2 by 4:

(-4 | 3 | -15

0 | 3 | 13)

Divide row 2 by 3:

(-4 | 3 | -15

0 | 1 | 13/3)

Subtract 3 × (row 2) from row 1:

(-4 | 0 | -28

0 | 1 | 13/3)

Divide row 1 by -4:

(1 | 0 | 7

0 | 1 | 13/3)

Collect results:

 {x = 7 . y = 13/3

step-by-step explanation:

i hate black

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents