Question

Помогите пожалуйста решить систему методом сложения x+y=4;3x+y=6

Answer 1

X+y=4
3x+y=6

х=4-у
3(4-у)+у=6
12-3у+у=6
12-2у=6
-2у=6-12
-2у=-6
у=3
х+3=4
х=1

Answer 2

Solution to the System of Equations

To solve the system of equations using the method of addition, we have the following equations:

Equation 1: x + y = 4 (1) Equation 2: 3x + y = 6 (2)

To eliminate one variable, we can multiply Equation 1 by 3 and Equation 2 by -1, and then add the two equations together. This will eliminate the y variable.

Multiplying Equation 1 by 3: 3(x + y) = 3(4) 3x + 3y = 12 (3)

Multiplying Equation 2 by -1: -1(3x + y) = -1(6) -3x - y = -6 (4)

Adding Equations 3 and 4: (3x + 3y) + (-3x - y) = 12 + (-6) 0x + 2y = 6 2y = 6 y = 3

Now that we have the value of y, we can substitute it back into Equation 1 to find the value of x.

Substituting y = 3 into Equation 1: x + 3 = 4 x = 4 - 3 x = 1

Therefore, the solution to the system of equations is x = 1 and y = 3.

Solution Verification

To verify the solution, we can substitute the values of x and y back into the original equations and check if they hold true.

Substituting x = 1 and y = 3 into Equation 1: 1 + 3 = 4 4 = 4 (True)

Substituting x = 1 and y = 3 into Equation 2: 3(1) + 3 = 6 3 + 3 = 6 6 = 6 (True)

Since both equations hold true when x = 1 and y = 3, we can conclude that the solution is correct.

Therefore, the solution to the system of equations x + y = 4 and 3x + y = 6 is x = 1 and y = 3.