Question

Solve the system of equations -5x - 5y = -30 and 10x + 3y = -3.

Answer 1

The solution to the system of equations -5x - 5y = -30 and 10x + 3y = -3 is found by using the elimination method, resulting in x = -3 and y = 9.

Step-by-step explanation:

To solve the system of equations -5x - 5y = -30 and 10x + 3y = -3, we can use the method of substitution or elimination. Here, let's use the elimination method.

First, we simplify the first equation by dividing every term by -5 to make the coefficients of one of the variables (y in this case) the same:

• 
  
• (-5x - 5y) / -5 = -30 / -5
• 
  
• x + y = 6

Next, we multiply the newly obtained equation by -3 to get the coefficients of y in the second equation to match:

• 
  
• -3(x + y) = -3(6)
• 
  
• -3x - 3y = -18

Now we can add the second original equation 10x + 3y = -3 to the equation we just derived:

• 
  
• (-3x - 3y) + (10x + 3y) = -18 + (-3)
• 
  
• 7x = -21

Dividing both sides by 7 gives us the value of x:

• 
  
• x = -3

Now we substitute x into x + y = 6 to find y:

• 
  
• (-3) + y = 6
• 
  
• y = 6 + 3
• 
  
• y = 9

The solution to the system is x = -3 and y = 9.