Question

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Here is the Question:
The system y = 4x - 7 and 2y = ax + b has no solution. Determine the value(s) of a and b for which this is true.

Answer 1

Answer:

a = 8

b ≠ 18

Step-by-step explanation:

y = 4x - 7

2y = ax + b

For there to be no solution, the lines (if graphed) should be parallel meaning that their slopes are equal but the y-intercepts are different

y = mx +b is the equation of a line where m is the slope and b is the y-intercept

Multiply the first equation by 2

2y = 8x - 14

2y = ax + b

So a has to equal 8

b can be anything except 14 (otherwise the lines would be the same)

Answer 2

9514 1404 393

Answer:

• a = 8
• b ≠ -14

Step-by-step explanation:

Multiply the first equation by 2 and you get ...

  2y = 8x -14

Compare to the second equation ...

  2y = ax +b

The pair of equations will have no solution if they describe parallel lines. That is, a = 8 and b ≠ -14.

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For a ≠ 8, the lines will intersect and there will be one solution.

For a = 8 and b = -14, the lines will be coincident, and there will be infinite solutions.