Question

3x - y= -10. 3y + 2x = -3 Решите систему уравнений

Answer 1

Вот
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Answer 2

To solve the system of equations:

1. 3x - y = -10
2. 3y + 2x = -3

There are several methods to solve a system of equations, but here we'll use the substitution method.

Step 1: Solve one equation for one variable Let's solve equation (1) for y: 3x - y = -10 y = 3x + 10

Step 2: Substitute the expression for y into the other equation (equation 2): 3y + 2x = -3 3(3x + 10) + 2x = -3 Expand and simplify: 9x + 30 + 2x = -3 Combine like terms: 11x + 30 = -3

Step 3: Isolate x Subtract 30 from both sides to isolate x: 11x = -3 - 30 11x = -33

Step 4: Solve for x Divide both sides by 11 to find the value of x: x = -33 / 11 x = -3

Step 5: Find y Now that we have the value of x, we can find y by substituting it into either equation (1) or the expression we found for y: y = 3x + 10 y = 3(-3) + 10 y = -9 + 10 y = 1

Step 6: Check Let's check if the values of x and y satisfy both equations:

1. 3x - y = -10 3(-3) - 1 = -10 -9 - 1 = -10 -10 = -10 (True)

2. 3y + 2x = -3 3(1) + 2(-3) = -3 3 - 6 = -3 -3 = -3 (True)

Both equations are satisfied by the values x = -3 and y = 1. So, the solution to the system of equations is x = -3 and y = 1.