Question

Решить систему 4*(х+3у)=10 -4х+3у=5

Answer 1

4x+12y=10
-4x+3y=5   

-4x=5-3y
4x=3y-5

3y-5+12y=10
15y=10+5
15y=15
y=15:15
y=1
4x=3*1-5
4x=3-5
4x=-2
x=-2/4
x=-0,5

Answer 2

To solve the system of equations:

1. 4*(x + 3y) = 10
2. -4x + 3y = 5

We can use the method of substitution or elimination. Let's use the elimination method to eliminate one variable:

Step 1: Multiply the second equation by 4 to make the coefficients of y in both equations the same:

Original equation 2: -4x + 3y = 5 Multiply by 4: 4*(-4x + 3y) = 4 * 5 Simplify: -16x + 12y = 20

Now our system is:

1. 4*(x + 3y) = 10
2. -16x + 12y = 20

Step 2: Now, we can eliminate the variable "y" from the system by adding equation 1 and equation 2:

4*(x + 3y) + (-16x + 12y) = 10 + 20

Simplify the equation:

4x + 12y - 16x + 12y = 30

Combine the x and y terms:

-12x + 24y = 30

Step 3: Now, let's isolate one of the variables in this new equation. Let's solve for "y" in terms of "x":

-12x + 24y = 30 24y = 12x + 30 y = (12x + 30) / 24 y = (2x + 5) / 4

Step 4: Now that we have an expression for "y" in terms of "x", we can substitute it back into one of the original equations to solve for "x". Let's use equation 1:

4*(x + 3y) = 10

Substitute y with (2x + 5) / 4:

4*(x + 3*((2x + 5) / 4)) = 10

Now, simplify the equation:

4*(x + 3x + 15/4) = 10

4*(4x + 15/4) = 10

Distribute the 4:

16x + 15 = 10

Step 5: Now, isolate "x" on one side of the equation:

16x = 10 - 15

16x = -5

x = -5 / 16

Step 6: Finally, plug the value of "x" back into the expression we found for "y":

y = (2x + 5) / 4

y = (2 * (-5/16) + 5) / 4

y = (-5/8 + 5) / 4

y = (40 - 5) / 32

y = 35 / 32

So, the solution to the system of equations is:

x = -5/16 y = 35/32