Help please 1. Solve the system of equations using substitution. Show your work y= 6x +1 y=-2 +6x 2. Solve the system of equations using substitution. Show your work 2x-3y=-1 Y=x-1

Answer 1

Hi...

With regards to the 1st system of equations; y = 6x + 1 and y = -2 + 6x....there is NO solution.

The reason why there is NO solutions is because as you can see these line have the SAME slope (m) if you see that the equations are written in the form of y = mx + b. If you were to GRAPH these lines, you would find that they are actually PARALLEL and never intersect. For lines to have a solution set would mean that they would intersect at that point and that point would be the solution set. So for these two equations there is NO ordered point (x,y) that satisfies.

As for the 2nd system of equations; 2x - 3y = -1 and y = x - 1, you can definitely substitute the 2nd equation into the 1st and see that the solution set is x = 0 & y = -1 OR point (0, -1)

Hope this helps...

Answer 2

Hi Alexus,

Question 1 does not have a solution

For Question 2 -

In question 2 we know that y is equal to x - 1. The goal of the substitution method is to only have one variable in the equation at a time so that we can solve for it. Because we know that y = x - 1, here we would plug (x-1) in for y in the first equation. We would then solve for x, and once found plug our solution for x back into our y equation and solve for y.

2x-3y = -1

y = x - 1

2x - 3(x-1) = -1

2x -3x + 3 = -1

-x + 3 = -1

-x = -4

x = 4

y= x - 1

y = 4 - 1

y=3

Answer 3

6x+1 =-2+6x

1=-2 no value of x will make the equation true. No real or imaginary solutions, zero solutions, null set

UNLESS you say x= infinity or negative infinity, then there are two solutions (infinity,infinity) and (-infinity,-infinity) but "infinity" is not a number, not a real or imaginary number, it's just a limit that is never reached.

but infinity + 1 does = -2 plus infinity. Similarly negative infinity + 1 = -2+ negative infinity. Infinity plus any finite number is still "just" infinity. Same with negative infinity.

while infinity is not real or imaginary, it is a "surreal number" There are two surreal solutions to the equation.

infinity is "countable" while infinity^infinity is uncountable. You could get even more solutions with infinity raised to exponents, but those are not surreal numbers, not imaginary, not real.

2x-3y=-1

3y = 2x+1

y = (2/3)x + 1/3 = x-1

x/3 = 4/3

x = 4

y= 3 (4,3) is a unique solution