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Nataliya [291]
3 years ago
8

What is the x-value in the solution to this system of linear equations? 2x − y = 11 x + 3y = −5

Mathematics
1 answer:
Setler [38]3 years ago
4 0

Answer:

x = 4

Step-by-step explanation:

Given the 2 equations

2x - y = 11 → (1)

x + 3y = - 5 → (2)

Multiply (1) by 3 and add to (2) to eliminate the y- term

6x - 3y = 33 → (3)

Add (2) and (3) term by term to eliminate y, that is

7x = 28 ( divide both sides by 7 )

x = 4

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8090 [49]

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Answer:

  5x^2 +10x = -5

Step-by-step explanation:

The equation will have one solution when the discriminant is zero.

In standard form, the equation is ...

  ax^2 +10x -c = 0

The discriminant of the equation ax^2+bx+c=0 is  ...

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so the discriminant of your equation is ...

  10^2 -4a(-c) = 100 +4ac

We want that to be zero, so we require ...

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  ac = -25

Any pair of values of 'a' and 'c' that have a product of -25 will satisfy the requirement. As you state, one possible pair is a = 5 and c = -5. Putting these values into the given equation makes it ...

  5x^2 +10x = -5 . . . . . the equation with a=5, c=-5

_____

<em>Additional comment</em>

Your problem statement does not require that 'a' be non-zero. If <em>a=0</em>, then the equation will have one real solution for <em>any value of c</em>.

If you restrict the solutions to integers, then possibilities include ...

  (a, c) = (1, -25), (5, -5), (25, -1), (-25, 1), (-5, 5), (-1, 25)

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