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

User Erek
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1 Answer

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Answer:

1. Slope = -0.800/2.000 = -0.400

2. x-intercept = 7/4 = 1.75000

3. y-intercept = 7/10 = 0.70000

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

User Alex Christodoulou
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