Question

I have these questions for someone to answer

Answer 1

Answer:

a) No Solution

b)

x = -1

y = -1

c)

x = 6

y = -6

Step-by-step explanation:

a)

We can solve for one variable in the 2nd equation and substitute that into 1st equation. Let's solve for x in the 2nd equation, we have:

$x+y=3\\x=3-y$

Now putting this into 1st and solving for y:

$2x+2y=6\\2(3-y)+2y=6\\6-2y+2y=6\\NOTHING$

We see that we CANNOT solve this as the variable vanishes!!

This type of system of equations are dependent equations. This is basically 2 SAME LINE, so there is NO SOLUTION to this system of equations.

Note: we can take "2" common from all the terms of the first equation and we will get the 2nd exact equation. So we can't solve this system.

No Solution

b)

2nd equation is already given as y = SOMETHING, so we put this (substitute) into the 1st equation and solve for x:

$2y-8x=6\\2(-x-2)-8x=6\\-2x-4-8x=6\\-10x=10\\x=-1$

So, x = -1

Now we put this value in 2nd equation to find value of y:

$y=-x-2\\y=-(-1)-2\\y=1-2\\y=-1$

So y = -1

So solution to this system is:

x = -1

y = -1

c)

Elimination method means adding up 2 equations so that one variable eliminates and then we solve for the other. Then again use substitute to solve for the eliminated variable in any one of the original equations.

Looking at the problem, if we add up both equations, x will vanish (eliminate) so we can solve for y. Let's do this:

$-4x-2y=-12\\4x+8y=-24\\---------\\6y=-36\\y=-6$

Now we put y = -6 into suppose 1st equation and solve for x:

$-4x-2(-6)=-12\\-4x+12=-12\\-4x=-24\\x=6$

So the solution is:

x = 6

y = -6