solve and check by substitution give a geometric interpertation of the system and its solution

Question

solve and check by substitution and give a geometric interpertation of the system and its solution

 

 

6x-2y=22

5x+5y=-15

Answer 1

It would have been better if you had shown us what you have done so far. Instead, it seems to me that you are just trying to get your assignment/homework done by the tutors. 

 

How does one solve a system of equations by substitution?  We can solve the first equation with

respect to y, which yields

 

y = 3x-11  (*).

 

Now we replace this value for y in the second equation and we get

 

5x +5(3x-11) = -15

20x - 55 = -15

20x = 40

x = 2

 

Finally, replace this value for x in (*) and we find

y = 3(2)-11 = -5

 

 

So the solution of your system of equation is x=2, y=-5.  Not that complicated, after all.

 

As for the geometric interpretation,  an equation like 6x-2y =22 represents a line (which one?) and so does the equation  5x+5y=-15 (Again, I am letting it for you to write it explicitly) . Therefore, the solution represents the point where the two lines intersect each other.