Question

8x-33y=19 12x+55y=19

Answer 1

Ответ:

8х-33y=19

8x-33y-19=19-19

8x-33y-19=0

12x+55y=19

12x+55y-19=19-19

12x+55y-19=0

Answer 2

To solve this system of linear equations, you can use either the substitution method or the elimination method. I'll use the elimination method in this example.

Here are your two equations:

1. 8x - 33y = 19
2. 12x + 55y = 19

First, let's manipulate one of the equations to make it easier to eliminate one of the variables. We can do this by multiplying both sides of the first equation by 12 and the second equation by 8, which will make the coefficients of x in both equations equal:

1. (12)(8x - 33y) = (12)(19)
2. (8)(12x + 55y) = (8)(19)

This gives us:

1. 96x - 396y = 228
2. 96x + 440y = 152

Now, we can subtract the first equation from the second equation to eliminate x:

(96x + 440y) - (96x - 396y) = 152 - 228

This simplifies to:

836y = -76

Now, divide both sides by 836 to solve for y:

y = -76 / 836 y = -19 / 209

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

8x - 33y = 19 8x - 33(-19/209) = 19

Now, simplify and solve for x:

8x + (33 * 19/209) = 19 8x + (627/209) = 19

Subtract (627/209) from both sides:

8x = 19 - (627/209)

Now, calculate the right side:

8x = (209*19 - 627)/209 8x = (3981 - 627)/209 8x = 3354/209

Now, divide both sides by 8 to solve for x:

x = (3354/209) / 8 x = (3354/209) * (1/8) x = (3354/209) * (1/8)

Now, you can calculate the values of x and y:

x ≈ 2.018 y ≈ -19/209

So, the solution to the system of equations is approximately:

x ≈ 2.018 y ≈ -0.090

You can round these values as needed based on the level of precision required for your problem.