Question

Solve the system:
10r-4t=6
7r +5t=12

Answer 1

To solve the system of equations, multiply the equations to eliminate a variable, subtract to eliminate another variable, and then solve for the remaining variable.

Step-by-step explanation:

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

1. 
   
3. Multiply the first equation by 7 and the second equation by 10 to make the coefficients of 'r' the same:
4. 
   

• 
  
• 70r - 28t = 42
• 
  
• 70r + 50t = 120
• 
  

Subtract the second equation from the first equation to eliminate 'r':

• 
  
• (70r - 28t) - (70r + 50t) = 42 - 120
• 
  
• -78t = -78
• 
  
• t = 1
• 
  

Now substitute the value of 't' into one of the original equations to solve for 'r'. Let's use the first equation:

• 
  
• 10r - 4(1) = 6
• 
  
• 10r - 4 = 6
• 
  
• 10r = 10
• 
  
• r = 1
• 
  

Therefore, the solution to the system of equations is r = 1 and t = 1.

Answer 2

t=1

r=1

Step-by-step explanation:

10r-4t=6 equation 1

7r +5t=12 equation 2

using equation 1 we have:

10r-4t=6

10r = 6+4t

r= (6+4t)/10 equation 3

using equation 3 in equation 2 we have:

7((6+4t)/10)) +5t=12

4.2 + 2.8t +5t =12

7.8t = 12-4.2

7.8t= 7.8

t = 7.8/7.8

t=1

so we have:

r= (6+4(1))/10

r= 10/10

r=1