Question

1) ax+8y=12 18x-3y=-1​

Answer 1

Ответ:

30

Объяснение:

Answer 2

To solve this system of linear equations:

1. ax + 8y = 12
2. 18x - 3y = -1

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

First, you can multiply both sides of equation (1) by 3 to make the coefficients of y in both equations cancel each other out when added together:

1. 3(ax + 8y) = 3(12)
2. 18x - 3y = -1

Now, simplify equation (1):

3ax + 24y = 36

Now, you have the system:

1. 3ax + 24y = 36
2. 18x - 3y = -1

Next, you can multiply equation (2) by 8 to make the coefficients of y in both equations cancel each other out when added together:

1. 3ax + 24y = 36
2. 8(18x - 3y) = 8(-1)

Now, simplify equation (2):

144x - 24y = -8

Now, you have the system:

1. 3ax + 24y = 36
2. 144x - 24y = -8

Now, add equation (1) and equation (2) together to eliminate y:

(3ax + 24y) + (144x - 24y) = 36 - 8

Now, simplify the equation:

3ax + 144x = 28

Now, you have a single equation in one variable (x). To solve for x, you can isolate it:

3ax + 144x = 28

Factor out the common factor of x:

x(3a + 144) = 28

Now, divide both sides by (3a + 144) to solve for x:

x = 28 / (3a + 144)

So, the solution for x in terms of the parameter 'a' is:

x = 28 / (3a + 144)

To find the solution for y, you can substitute this value of x into either equation (1) or (2). Let's use equation (1):

3ax + 24y = 36

Substitute x = 28 / (3a + 144):

3a(28 / (3a + 144)) + 24y = 36

Now, simplify the equation and solve for y:

(84a / (3a + 144)) + 24y = 36

Multiply both sides by (3a + 144) to eliminate the fraction:

84a + 24y(3a + 144) = 36(3a + 144)

Now, simplify and solve for y:

84a + 72ay + 3456y = 108a + 5184

Rearrange terms:

72ay + 84a - 108a = 5184 - 3456y

Combine like terms:

72ay - 24a = 1728 - 3456y

Factor out a common factor of 24a:

24a(3y - 1) = 1728 - 3456y

Now, divide both sides by 24a to solve for y:

3y - 1 = (1728 - 3456y) / (24a)

3y = (1728 - 3456y) / (24a) + 1

Now, isolate y:

y = [(1728 - 3456y) / (24a) + 1] / 3

So, the solution for y in terms of the parameter 'a' is:

y = [(1728 - 3456y) / (24a) + 1] / 3