The sum of four times a number and 6 times a second number is 36. the difference between five times the second number and three times the first number is 49

This is a simple system of equations. We first write the words in math as 4x + 6y = 36 and 5y - 3x = 49.

Now we isolate 5 in the second equation to get 5y = 49+3x or y=(49+3x)/5. We can now substitute our value for y into our first equation and simplify.

4x + 6y = 36 is the same as 4x+6((49+3x)/5) = 36.  This can be simplified to 4x+(294+18x)/5 = 36, which is the same as 20x+294+18x = 180.  We can combine like terms to get 38x +294 = 180 or 38x = -114. Now we divide by 38 on both sides to get x = -3.

Now that we have our value for x, we substitute that value into the second equation and solve for y.

5y - 3x = 49 is the same as 5y - 3(-3) = 49 or 5y+9 = 49.  This can be simplified to 5y=40 or y=8.

Our values for x and y are -3 and 8.  Hope this helps!