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fomenos
3 years ago
13

6. 4x + 2y = 16 | 5x - 2y = 38

Mathematics
1 answer:
Zolol [24]3 years ago
4 0

Answer:

1. Slope = -4.000/2.000 = -2.000

 x-intercept = 8/2 = 4

 y-intercept = 8/1 = 8.00000

2.  Slope = 5.000/2.000 = 2.500

 x-intercept = 38/5 = 7.60000

 y-intercept = 38/-2 = 19/-1 = -19.00000

Step-by-step explanation:

1.

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  4x + 2y - 16  =   2 • (2x + y - 8)

Equation at the end of step  1  :

Step  2  :

Equations which are never true :

2.1      Solve :    2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Equation of a Straight Line

2.2     Solve   2x+y-8  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  2x+y-8  = 0 and calculate its properties

Graph of a Straight Line :

 

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 8/1 so this line "cuts" the y axis at y= 8.00000

 y-intercept = 8/1  =  8.00000

Calculate the X-Intercept :

When y = 0 the value of x is 4/1 Our line therefore "cuts" the x axis at x= 4.00000

 x-intercept = 8/2  =  4

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 8.000 and for x=2.000, the value of y is 4.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 4.000 - 8.000 = -4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     = -4.000/2.000 = -2.000

Geometric figure: Straight Line

 Slope = -4.000/2.000 = -2.000

 x-intercept = 8/2 = 4

 y-intercept = 8/1 = 8.00000

Processing ends successfully

2.

Step  1  :

Equation of a Straight Line

1.1     Solve   5x-2y-38  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  5x-2y-38  = 0 and calculate its properties

Graph of a Straight Line :

 

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 19/-1 so this line "cuts" the y axis at y=-19.00000

 y-intercept = 38/-2 = 19/-1  = -19.00000

Calculate the X-Intercept :

When y = 0 the value of x is 38/5 Our line therefore "cuts" the x axis at x= 7.60000

 x-intercept = 38/5  =  7.60000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -19.000 and for x=2.000, the value of y is -14.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -14.000 - (-19.000) = 5.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  5.000/2.000 =  2.500

Geometric figure: Straight Line

 Slope = 5.000/2.000 = 2.500

 x-intercept = 38/5 = 7.60000

 y-intercept = 38/-2 = 19/-1 = -19.00000

Processing ends successfully

plz mark me as brainliest :)

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Solving

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As a check

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