1. ## Solutions to equations

Can you show me how to go about solving these problems? I'm suppose to translate the given information into a system of equations and solve the system to determine the two numbers.

#1. One number exceeds a second number by 8. Three-fourths of the larger number is 3 more than the smaller number.

With the problem #2, I want to make sure I'm doing it right.
I'm suppose to determine whether each ordered pair is a solution of the given system of linear equations.

#2 (-0.5,0)

2x+3y=3
8x=12y-4

When I plug (-0.5,0) into the equation I get

2(-0.5) + 3(0)=3
-3 = 3 ,

8(-0.5) = 12(0)-4
- 4.0 = 4
-4 = -4 ,

So would (-0.5,0) not be a solution to both equations since one 3 is negative and the other is a positive 3? I know it would of been a solution if it was -4 = -4 and the other was 3 = 3, but I'm not sure since one three is negative.

2. Originally Posted by Ash
Can you show me how to go about solving these problems? I'm suppose to translate the given information into a system of equations and solve the system to determine the two numbers.

#1. One number exceeds a second number by 8. Three-fourths of the larger number is 3 more than the smaller number.

With the problem #2, I want to make sure I'm doing it right.
I'm suppose to determine whether each ordered pair is a solution of the given system of linear equations.

#2 (-0.5,0)

2x+3y=3
8x=12y-4

When I plug (-0.5,0) into the equation I get

2(-0.5) + 3(0)=3
-3 = 3 ,

8(-0.5) = 12(0)-4
- 4.0 = 4
-4 = -4 ,

So would (-0.5,0) not be a solution to both equations since one 3 is negative and the other is a positive 3? I know it would of been a solution if it was -4 = -4 and the other was 3 = 3, but I'm not sure since one three is negative.
#1 Let x and y be the two numbers, assuming that x is the largest.
Since"One number exceeds a second number by 8. ",
x=y+8
the second sentence provides the second equation:"Three-fourths of the larger number is 3 more than the smaller number."
3/4x=y+3
solving the system you have the solution: x=20, y=12

3. #2 You are right, the pair is not a solution .
Pay attention when evaluating expresion. respect the order of operation. Multiplication first, then addition.
2(-0.5) + 3(0)=3
-1+0=3
-1=3 is not true, so right away you can say that the pair is not a solution.

4. Originally Posted by alinailiescu
#1 Let x and y be the two numbers, assuming that x is the largest.
Since"One number exceeds a second number by 8. ",
x=y+8
the second sentence provides the second equation:"Three-fourths of the larger number is 3 more than the smaller number."
3/4x=y+3
solving the system you have the solution: x=20, y=12
Thanks for your help, I now see where I went wrong on the second problem, but can you show me the steps in how you came up with x= 20 and y=12 ?

5. You have the system:
x=y+8
3/4x=y+3
using substitution method, by writting y+8 (from the first equation) insted of x into the second we have:
3/4(y+8)=y+3
3/4y+6=y+3
6-3=y-3/4y
3=1/4y
12=y,
using this value into the first equation we have x=12+8so, x=20