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What value of b will cause the system to have an infinite number of solutions? Y=6x+b -3x+1/2y=-3

1 Answer

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Answer:

b = -6

Explanation:

Given:

y=6x+b ----- (eq 1)

and

-3x+1/2y=-3 (Rearrange this equation to look likes eq (1) , add -3x to both sides)

(1/2) y = 3x - 3 (multiply both sides by 2)

y = 2(3x -3) (distribute the 2 into parentheses)

y = 6x - 6 -----(eq 2)

Recall that a system of equations will have an infinite number of solutions if both equations are the same line. (i.e they have the same slope and y intercept)

In our case, if you compare eq 1 and eq 2, the way to make both equations the same line is if b = -6. (this is the answer)

User Farid Imranov
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