Question

4) 2x+13y=-69, 14x+11y=-3.​

Answer 1

Ответ:

(4,5; -6)

Пошаговое объяснение:

{2х + 13у = -69 | * (-7)

{14х + 11у = -3

{-14х - 91у = 483

{14х + 11у = -3

{-80у = 480

{14х + 11у = -3

1)

-80у = 480

у = 480 : (-80)

у = -6

2)

14х + 11у = -3

14х + 11 * (-6) = -3

14х - 66 = -3

14х = -3 + 66

14х = 63

х = 63 : 14

х = 4,5

Answer 2

To solve this system of linear equations:

1. 2x + 13y = -69
2. 14x + 11y = -3

You can use the method of either substitution or elimination. I'll use the elimination method:

First, we need to make the coefficients of either x or y in both equations the same (or multiples of each other) so that we can eliminate one variable when we subtract the equations. In this case, it's easier to eliminate x. To do that, we can multiply both sides of the first equation by 7 and the second equation by -1 so that the coefficients of x in both equations become equal:

1. 14x + 91y = -483
2. -14x - 11y = 3

Now, add the two equations together to eliminate x:

(14x + 91y) + (-14x - 11y) = (-483) + 3

This simplifies to:

80y = -480

Now, divide both sides by 80 to isolate y:

y = -480 / 80 y = -6

Now that we've found the value of y, substitute it back into either of the original equations to solve for x. Let's use the first equation:

2x + 13y = -69 2x + 13(-6) = -69 2x - 78 = -69

Now, add 78 to both sides:

2x - 78 + 78 = -69 + 78 2x = 9

Finally, divide both sides by 2 to solve for x:

2x / 2 = 9 / 2 x = 9 / 2 x = 4.5

So, the solution to the system of equations is:

x = 4.5 y = -6