DonniceLifesaver
I just want to know if my answer right?? Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this. 10x – y = 12.5 3x + y = 7
x=1.5
y=2.5
Your Welcome :)
To solve this system of equations using the elimination method, follow these steps:
1. Start with the given system of equations:
10x – y = 12.5 ...(Equation 1)
3x + y = 7 ...(Equation 2)
2. Choose one of the variables to eliminate. In this case, let's eliminate the y-variable.
3. Multiply Equation 2 by -1 to make the y-terms cancel each other out:
-1 * (3x + y) = -1 * 7
-3x - y = -7 ...(Equation 3)
Now we have Equation 1: 10x – y = 12.5
Equation 3: -3x - y = -7
4. Add both equations (Equation 1 + Equation 3) to eliminate the y-term:
(10x – y) + (-3x - y) = 12.5 + (-7)
10x - 3x - y + y = 12.5 - 7
7x = 5.5
5. Solve for x by dividing both sides of the equation by 7:
7x/7 = 5.5/7
x = 0.7857 (rounded to 4 decimal places)
6. Substitute the found value of x into either Equation 1 or Equation 2 to solve for y. Let's use Equation 2:
3x + y = 7
3(0.7857) + y = 7
2.3571 + y = 7
y = 7 - 2.3571
y = 4.6429 (rounded to 4 decimal places)
So, the solution to the system of equations is x = 0.7857 and y = 4.6429.