use the linear combination method to solve the system of equations. explain each step of your solution. 3x-8y=7 x+2y=-7

1. Slope = -0.800/2.000 = -0.400

2. x-intercept = 7/4 = 1.75000

3. y-intercept = 7/10 = 0.70000

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    3*x-8*y-(7*x+2*y-7)=0

Step by step solution :

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  -4x - 10y + 7  =   -1 • (4x + 10y - 7)

Equation at the end of step  1  :

Step  2  :

Equation of a Straight Line

2.1     Solve   -4x-10y+7  = 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  -4x-10y+7  = 0 and calculate its propertie

Notice that when x = 0 the value of y is 7/10 so this line "cuts" the y axis at y= 0.70000

 y-intercept = 7/10  =  0.70000

Calculate the X-Intercept :

When y = 0 the value of x is 7/4 Our line therefore "cuts" the x axis at x= 1.75000

 x-intercept = 7/4  =  1.75000

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 0.700 and for x=2.000, the value of y is -0.100. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -0.100 - 0.700 = -0.800 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     = -0.800/2.000 = -0.400