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Alchen [17]
3 years ago
12

Solve the following system of equations and select the correct answer below:

Mathematics
1 answer:
Sauron [17]3 years ago
5 0
3x + 3y + 2z = -5 ⇒ 3x + 3y + 2z = -5 ⇒ 3x + 3y + 2z =   -5
1x + 1y + 3z = -4 ⇒ 1x + 1y + 3z = -4 ⇒ 3x + 3y + 9z = -12
3x -  1y + 5z = -8                                                    -7z = 7
                                                                                -7    -7
                                                                                  z = -1
3x + 3y + 2z = -5                                                      
1x + 1y + 3z = -4 ⇒ 1x + 1y + 3z = -4
3x -  1y + 5z = -8 ⇒ 3x -  1y + 5z = -8
                                        4x + 8z = -12     

     4x + 8z = -12
 4x + 8(-1) = -12
       4x - 8 = -12
           + 8    + 8
            4x = -4
             4      4
              x = -1

        3x + 3y + 2z = -5
3(-1) + 3y + 2(-1) = -5
           -3 + 3y - 2 = -5
             3y - 3 - 2 = -5
                  3y - 5 = -5
                      + 5  + 5
                       3y = 0
                        3     3
               (x, y, z) = (-1, 0, -1)
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Which equation represents a line that passes through the point ( 6 , − 3 ) and is parallel to the graph of y = 3 x + 1 ?
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Answer:

              y + 3= 3(x - 6)        ←    point-slope form

             y = 3x - 21           ←    slope-intercept form

             3x - y = 21         ←    standard form

Step-by-step explanation:

The point-slope form of the equation of line it's y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point the line passing through.

y=m₁x+b₁   ║   y=m₂x+b₂   ⇔    m₁ = m₂

{Two lines are parallel if  their slopes are equal}

y = 3x + 1   ⇒    m₁ = 3    ⇒    m₂ = 3

(6, -3)    ⇒    x₁ = 6,  y₁ = -3

point-slope form:

y - (-3) = 3(x - 6)

y + 3 = 3(x - 6)

y + 3 = 3x - 18              {subtact 3 from both sides}

y = 3x - 21        ←    slope-intercept form

-3x + y = -21                 {multiply both sides by (-1)}

3x - y = 21         ←    standard form

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