Question

1)5x – y + 14 = 0,x + 2y - 6 = 0;​

Answer 1

Пошаговое объяснение:

5x – y + 14 = 0,

x + 2y - 6 = 0

x=-2y+6

5(-2y+6)-y+14=0

-10y+30-y+14=0

-11y=-44

y=4

x=-2y+6

x=-2×4+6=-8+6=-2

Ответ:( x,y)=(-2,4)

Answer 2

To solve this system of linear equations, you can use either the substitution method or the elimination method. I'll show you how to solve it using the elimination method.

Given equations:

1. 5x - y + 14 = 0
2. x + 2y - 6 = 0

We can eliminate one of the variables by multiplying one or both equations by a suitable factor so that when we add or subtract them, one variable cancels out. In this case, we'll eliminate y. To do that, we'll multiply the second equation by 5 to make the coefficients of y in both equations cancel each other out:

1. 5x - y + 14 = 0
2. 5(x + 2y - 6) = 5(0)

Now, we have:

1. 5x - y + 14 = 0
2. 5x + 10y - 30 = 0

Next, subtract equation 3 from equation 1 to eliminate y:

(5x - y + 14) - (5x + 10y - 30) = 0 - 0

This simplifies to:

5x - y + 14 - 5x - 10y + 30 = 0

Now, combine like terms:

-11y + 44 = 0

Now, isolate -11y:

-11y = -44

To solve for y, divide both sides by -11:

y = -44 / -11 y = 4

Now that you have the value of y, you can substitute it into one of the original equations to solve for x. Let's use equation 1:

5x - y + 14 = 0 5x - 4 + 14 = 0

Now, simplify and solve for x:

5x + 10 = 0

Subtract 10 from both sides:

5x = -10

Divide both sides by 5 to isolate x:

x = -10 / 5 x = -2

So, the solution to the system of equations is:

x = -2 y = 4