Mathematics, 24.02.2020 20:40 bmr12

Given 3p+2q=3 and 6p+8q=2 solve for q and p simultaneously

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Answer from: cieswa46054

Slope = -5.000/2.000 = -2.500

p-intercept = 2/15 = 0.13333

q-intercept = 2/6 = 1/3 = 0.33333

Step-by-step explanation:

Step 1 :

Pulling out like terms :

1.1 Pull out like factors :

-15p - 6q + 2 = -1 • (15p + 6q - 2)

Equation at the end of step 1 :

Step 2 :

Equation of a Straight Line

2.1 Solve -15p-6q+2 = 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 axi

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line -15p-6q+2 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when p = 0 the value of q is 1/3 so this line "cuts" the q axis at q= 0.33333

q-intercept = 2/6 = 1/3 = 0.33333

Calculate the X-Intercept :

When q = 0 the value of p is 2/15 Our line therefore "cuts" the p axis at p= 0.13333

p-intercept = 2/15 = 0.13333

Calculate the Slope :

Slope is defined as the change in q divided by the change in p. We note that for p=0, the value of q is 0.333 and for p=2.000, the value of q is -4.667. So, for a change of 2.000 in p (The change in p is sometimes referred to as "RUN") we get a change of -4.667 - 0.333 = -5.000 in q. (The change in q 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

p-intercept = 2/15 = 0.13333

q-intercept = 2/6 = 1/3 = 0.33333

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Given 3p+2q=3 and 6p+8q=2 solve for q and p simultaneously...