Question

Determine if the following system of equations has no solutions, infinitely many

solutions or exactly one solution.
One Solution
-4x + y = 1
-16x5y = 8
Infinitely Many Solutions
No Solutions
?

Answer 1

One solution

Explanation:

You do not have an addition or subtraction sign between -16x and 5y. I am assuming that you mean addition.

Take -4x + y = 1 and multiply it all through by -4

16x - 4y = -4 Add this to the second equation

-16x + 5y = 8

y = 4

Substitute 4 for y in either of the two original equations.

-4x + y = 1

-4x + 4 = 1 Subtract 4 from both sides

-4x + 4 - 4 = 1 - 4

-4x = -3 Divide both sides by -4

x =
`(3)/(4)`

The solution is (
`(3)/(4)`, 4)

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