Question

Use elimination to solve each system of equations: 6x + 5Y = 4 6x - 7y = -20

Answer 1

tep  1  :Equation of a Straight Line

 1.1     Solve   6x+5y-4  = 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  6x+5y-4  = 0 and calculate its properties

Graph of a Straight Line : Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 4/5 so this line "cuts" the y axis at y= 0.80000

  y-intercept = 4/5 = 0.80000 Calculate the X-Intercept :

When y = 0 the value of x is 2/3 Our line therefore "cuts" the x axis at x= 0.66667

  x-intercept = 4/6 = 2/3 = 0.66667 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 0.800 and for x=2.000, the value of y is -1.600. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -1.600 - 0.800 = -2.400 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)