Explain EACH step you would take to solve the following system using substitution. y = 3x - 5
x = 2

Step-by-step explanation:

Use the slope-intercept form to find the slope and y-intercept.  

The slope-intercept form is  y = m x + b , where  m  is the slope and  b  is the y intercept.

y = m x + b

Find the values of  m  and  b  using the form  y = m x + b .

m =− 5 3 b = 2

The slope of the line is the value of  m , and the y-intercept is the value of  b .

Slope:  

− 5 3

y-intercept:  2

Any line can be graphed using two points. Select two  x  values, and plug them into the equation to find the corresponding  y  values.

Choose  0  to substitute in for  x  to find the ordered pair.

Replace the variable  x  with  0  in the expression.

f ( 0 ) = − 5 ( 0 ) 3 + 2

Simplify the result.

Simplify each term.

Cancel the common factor of  0  and  3 .

Factor  3  out of  5 ( 0 ) .

f ( 0 ) = − 3 ( 5 ⋅ ( 0 ) ) 3 + 2

Cancel the common factors.

Factor  3  out of  3 .

f ( 0 ) = − 3 ( 5 ⋅ ( 0 ) ) 3 ( 1 ) + 2

Cancel the common factor.

f ( 0 ) = − 3 ( 5 ⋅ ( 0 ) ) 3 ⋅ 1 + 2

Rewrite the expression.

f ( 0 ) = − 5 ⋅ ( 0 ) 1 + 2

Divide  5 ⋅ ( 0 )  by  1 .

f ( 0 ) = − ( 5 ⋅ ( 0 ) ) + 2

Multiply  5  by  0 .

f ( 0 ) = − 0 + 2

Multiply  − 1  by  0 .

f ( 0 ) = 0 + 2

Add  0  and  2 .

f ( 0 ) = 2

The final answer is  2 .

2

The  y  value at  x = 0  is  2 .

y = 2

Choose  3  to substitute in for  x  to find the ordered pair.  

Replace the variable  x  with  3  in the expression.

f ( 3 ) = − 5 ( 3 ) 3 + 2

Simplify the result.

Simplify each term.

Cancel the common factor of  3 .

Cancel the common factor.

f ( 3 ) = − 5 ⋅ 3 3 + 2

Divide  5  by  1 .

f ( 3 ) = − 1 ⋅ 5 + 2

Multiply  − 1  by  5 .

f ( 3 ) = -5 +2

Add  − 5  and  2 .

f ( 3 ) = − 3

The final answer is  − 3 .

− 3

The  y  value at  x = 3  is  − 3 .

y = − 3

Create a table of the  x  and  y  values.

x-   0,  3

y- 2, -3

Graph the line using the slope and the y-intercept, or the points.

Slope:   − 5 /3

y-intercept:  2

x- 0, 3

y- 2, -3

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

if you're trying to figure out how much each ounce cost it would be 0.20

cents each ounce