60urgent
use the linear combination method to solve the system of equations. explain each step of your solution.
3x-8y=7
x+2y=-7

Using linear combination method to solve the system of equations 3x - 8y = 7  and x + 2y = -7 is (x, y) = (-3, -2)

Given that, a system of equations are:

3x – 8y = 7 ⇒ (1) and x + 2y = - 7 ⇒ (2)

We have to solve the system of equations using linear combination method and find their solution.

Linear combination is the process of adding two algebraic equations so that one of the variables is eliminated. Addition or subtraction can be used to perform a linear combination.

Now, let us multiply equation (2) with 4 so that y coefficients will be equal numerically.

4x + 8y = -28 ⇒ (3)

Now, add (1) and (3)  

3x – 8y = 7  

4x + 8y = - 28  

7x + 0 = - 21  

7x = -21  

x = - 3  

Now, substitute "x" value in (2)

(2) ⇒ -3 + 2y = - 7  

2y = 3 – 7  

2y = - 4  

y = -2

Hence, the solution for the given two system of equations is (-3, -2)

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."