Question

X+2y=5-x+7y=13решите систему уравнения

Answer 1

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Answer 2

To solve the system of equations, you can use the method of substitution or elimination. Let's use the method of substitution:

Given system of equations:

1. x + 2y = 5
2. -x + 7y = 13

Step 1: Solve one of the equations for one variable in terms of the other variable. Let's solve equation 1) for x: x = 5 - 2y

Step 2: Substitute the expression for x into the second equation (equation 2): -(5 - 2y) + 7y = 13

Step 3: Simplify and solve for y: -5 + 2y + 7y = 13 9y - 5 = 13 9y = 13 + 5 9y = 18 y = 18 / 9 y = 2

Step 4: Now that we have the value of y, substitute it back into the expression we found for x in Step 1: x = 5 - 2y x = 5 - 2(2) x = 5 - 4 x = 1

Step 5: Check the solution by substituting the values of x and y into both equations:

1. x + 2y = 5 1 + 2(2) = 1 + 4 = 5 (True)

2. -x + 7y = 13 -(1) + 7(2) = -1 + 14 = 13 (True)

Both equations hold true when x = 1 and y = 2, so the solution to the system of equations is x = 1 and y = 2.