## Which system of equations below has exactly one solution? y=-8x – 6 and y = –8x + 6 y=-8x – 6 and 1/2y = -4x – 3 y=-8x – 6

Question

Which system of equations below has exactly one solution?
y=-8x – 6 and y = –8x + 6
y=-8x – 6 and 1/2y = -4x – 3
y=-8x – 6 and y = 8x – 6
y = -8x – 6 and -y = 8x + 6

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4 months 2022-01-31T03:24:06+00:00 1 Answer 0 views 0

(y = -8x – 6  and  y = 8x – 6) will have exactly one solution.

Step-by-step explanation:

1) Check number of solutions for A (using substitution)

y = -8x -6

y = -8x + 6

-8x – 6 = -8x + 6

+8x         +8x

0 – 6 = 0 + 6

-6 = 6 (since this is false, it would be no solution)

2) Check number of sultions for B (using substition)

y = -8x – 6

1/2y = -4x -3

y = -8x – 6 (Multiply both sides of second equation by 2 to cancel out fraction on left side)

-8x – 6 = -8x – 6

Since this is the same equation on both sides- when you cancel everything out it will be 0=0, meaning infinite solution

3) Check number of solutions for C (using substition)

y = -8x – 6

y = 8x – 6

-8x – 6 = 8x – 6

+8x   +6 = +8x +6

0 = 16x

x=0

The X value for the solution is 0, when we plug in this X value into one of the equations and solve for Y we will be able to get the Y coordinate

y = -8(0) – 6

y = -6

The solution for C will by (0,-6) which is one solution.

4) Check number of solutions for D (using substition)

y = -8x – 6

-y = 8x +6 –> y = -8x -6

muiltiply both sides of second equation by -1 to make the y positive

-8x – 6 = -8x – 6

Since this is the same equation on both sides- when you cancel everything out it will be 0=0, meaning infinite solution