Solve the equation 3y=11-2x,3x=y-11

Question

solve equation 3y=11-2x,3x=y-11 using any algebraic method.

Answer 1

Rearrange the equations so that the x and y terms are on the same side.

 

3y=11-2x  becomes  2x+3y=11

3x=y-11    becomes  3x-y =-11

 

Lets multiply equation 2 by 3, and keep equation 1 as is it.  We end up with

 

  2x+3y=11

9x-3y=-33

 

Now we add the equations to eliminate the y terms.  We obtain

 

11x = -22

 

 x = -2

 

Substitute this value into the original equation and solve for y.

 

 

 

 

 

Answer 2

From equation 2 -------------> y = 3x + 11

 

Substitute in equation 1 -----> 9x + 33 = 11 - 2x

 

11x = -22 ----> x = -2 ----> y = -6 + 11 = 5

Answer 3

Given: equation A is 3y = 11 - 2x; equation B is 3x = y - 11

step 1. rearrange equation B to y = 3x = + 11

step 2. substitute the value of y from equation B into equation A; equation A becomes 3(3x + 11) = 11 - 2x

step 3. expand equation A to 9x + 33 = 11 - 2x

step 4. combine the values in equation A to 9x + 2x = 11 - 33

step 5. solve equation A for x = -2

step 6. substitute the value for x into equation A, which becomes 3y = 11 -2(-2)

step 7. expand that equation to 3y = 15

step 8. solve for y = +5.

step 9. PROOF: substitute the value for y into equation A, which becomes 3(+5) = 11 - 2x, but the value for x is -2, so the equation becomes 3(+5) = 11 -2(-2) yielding 15 = 15

 

so, the value for y is +5, and the value for x is -2