Question

A)y=-7x+9 и y=x+6 b)y=3x+5 и y=6x+10 c)y=-4 и y=-x-8 d)y=0,5+5 и y=2x+6 e)y=-6+3 и y=-6x-7

Answer 1

Ответ:

$1)\ \ \left\{\begin{array}{l}y=-7x+9\\y=x+6\end{array}\right\ \ \left\{\begin{array}{l}-7x+9=x+6\\y=x+6\end{array}\right\ \ \left\{\begin{array}{l}-8x=-3\\y=x+6\end{array}\right\ \ \left\{\begin{array}{l}x=\dfrac{3}{8}\\y=6\dfrac{3}{8}\end{array}\right$

$2)\ \ \left\{\begin{array}{l}y=3x+5\\y=6x+10\end{array}\right\ \ \left\{\begin{array}{l}3x+5=6x+10\\y=6x+10\end{array}\right\ \ \left\{\begin{array}{l}3x=-5\\y=6x+10\end{array}\right\ \ \left\{\begin{array}{l}x=-\dfrac{5}{3}\\y=0\end{array}\right$

$3)\ \ \left\{\begin{array}{l}y=-4\\y=-x-8\end{array}\right\ \ \left\{\begin{array}{l}y=-4\\x=-y-8\end{array}\right\ \ \left\{\begin{array}{l}y=-4\\x=-4\end{array}\right$

$4)\ \ \left\{\begin{array}{l}y=0,5+5\\y=2x+6\end{array}\right\ \ \left\{\begin{array}{l}y=5,5\\2x=y-6\end{array}\right\ \ \left\{\begin{array}{l}y=5,5\\2x=-0,5\end{array}\right\ \ \left\{\begin{array}{l}y=5,5\\x=-0,25\end{array}\right$

$5)\ \ \left\{\begin{array}{l}y=-6+3\\y=-6x-7\end{array}\right\ \ \left\{\begin{array}{l}y=-3\\6x=-y-7\end{array}\right\ \ \left\{\begin{array}{l}y=-3\\6x=-4\end{array}\right\ \ \left\{\begin{array}{l}y=-3\\x=-\dfrac{2}{3}\end{array}\right$

Answer 2

To solve these systems of equations, you need to find the values of x and y that satisfy both equations in each system. Let's go through each of the options:

a) y = -7x + 9 and y = x + 6

To solve this system, set the two equations equal to each other:

-7x + 9 = x + 6

Now, solve for x:

-7x - x = 6 - 9 -8x = -3

Divide both sides by -8:

x = (-3) / (-8) x = 3/8

Now that you have found the value of x, you can find y using one of the original equations. Let's use the second equation:

y = x + 6 y = (3/8) + 6

Now, calculate y:

y = 3/8 + 48/8 y = 51/8

So, the solution to this system is x = 3/8 and y = 51/8.

b) y = 3x + 5 and y = 6x + 10

Set the two equations equal to each other:

3x + 5 = 6x + 10

Now, solve for x:

3x - 6x = 10 - 5 -3x = 5

Divide both sides by -3:

x = 5 / -3 x = -5/3

Now, find y using one of the original equations. Let's use the first equation:

y = 3x + 5 y = 3(-5/3) + 5

Calculate y:

y = -5 + 5 y = 0

So, the solution to this system is x = -5/3 and y = 0.

c) y = -4 and y = -x - 8

Since both equations are linear and have the same y-value, they are parallel lines, and there is no point of intersection. This system has no solution.

d) y = 0.5x + 5 and y = 2x + 6

Set the two equations equal to each other:

0.5x + 5 = 2x + 6

Now, solve for x:

0.5x - 2x = 6 - 5 -1.5x = 1

Divide both sides by -1.5:

x = 1 / -1.5 x = -2/3

Now, find y using one of the original equations. Let's use the first equation:

y = 0.5x + 5 y = 0.5(-2/3) + 5

Calculate y:

y = (-1/3) + 5 y = 14/3

So, the solution to this system is x = -2/3 and y = 14/3.

e) y = -6 + 3 and y = -6x - 7

Simplify both equations:

y = -3 and y = -6x - 7

Since both equations have the same y-value (-3), they represent parallel lines, and there is no point of intersection. This system has no solution.