A system of equations has 1 solution. If 4x - y = 5 is one of the equations, which could be the other equation?

AN

y = 4x + 5

y = 4x - 5

2y = 8x - 10

-2y = -8x - 10

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Corrected Options

(A)y = –4x + 5

(B)y = 4x – 5

(C)2y = 8x – 10

(D)–2y = –8x – 10

(A)y = –4x + 5

Step-by-step explanation:

A system of linear equations has one solution when the graphs of the two equations intersect at a point.

Given our first equation:

4x-y=5 which is the same as y=4x-5

In Option B, the line is exactly the same line, therefore the system of equation will have infinite solutions.In Option C, 2y=8x-10 is equivalent to y=4x-5, likewise yielding infinite solutions like Option B.In option D, –2y = –8x – 10 is equivalent to y=4x+5. This pair will yield no solution.

Consider Option A: y = –4x + 5

Solving y = –4x + 5  and y=4x-5

–4x + 5=4x-5

-8x=-10

x=1.25

y=–4(1.25) + 5 =0

x=1.25, y=0

Thus option A is the only equation which could be the other equation

It has a slope of 1 nd a y intercept of -2