How do you solve the following system: #8x-3y=3, x+3y=3

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Question

How do you solve the following system: #8x-3y=3, x+3y=3

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Ethan Adkins · Accepted Answer

This ordered pair is #(2/3, 7/9)# or #(0.bar6, 0.bar7)#.

Use the elimination method, and then substitution to solve. Line up the two equations, one on top of the other: #8x - 3y = 3# #color(white)(8)##x + 3y = 3# Now add them together, and notice that #y# will be eliminated because #-3y + 3y = 0#: #8x color(blue)(- 3y) = 3# #color(white)(8)##x color(blue)(+ 3y) = 3# #color(white)(x)9x color(white)(+ 0y) = 6# #9x = 6# #x = 6/9 rarr 2/3# Now substitute that value for #x# into another equation, and solve for #y#: #x + 3y = 3# #2/3 + 3y = 3# #2 + 3(3)y = 3(3)# #2 + 9y = 9# #9y = 7# #y = 7/9# So this ordered pair is #(2/3, 7/9)#. As a repeating decimal, the coordinates are #(0.bar6, 0.bar7)#.

Ethan Adkins · Answer

Solution: # x= 2/3 and y= 7/9# #8 x-3 y=3 ; (1) , x +3 y =3; (2)# , adding equation (1) and equation (2) we get, # 9 x = 6 :. x = 6/9 or x= 2/3# Putting #x=2/3# in equation (2) we get, #2/3 +3 y =3; # or #3 y =3- 2/3 or 3 y = 7/3 or y = 7/9 # Solution: # x= 2/3 and y= 7/9# [Ans]

Hazel Anglin · Answer

undefined To solve the system of equations:

1. Use the method of elimination or substitution to find the values of x and y that satisfy both equations simultaneously.
2. Add or subtract the equations to eliminate one of the variables.
3. Solve for the remaining variable.
4. Substitute the value of the remaining variable into one of the original equations to find the value of the other variable.
5. Check the solution by substituting the values of x and y into both equations to ensure they satisfy both equations simultaneously.