solve 2x-3y plus 2 equals x plus 2y minus 5 equals 3x plus y?
To solve this system of equations, we need to find the values of x and y that satisfy all three equations. Here's how we can do it step by step:
1. Write down the given equations:
- Equation 1: 2x - 3y + 2 = x + 2y - 5
- Equation 2: x + 2y - 5 = 3x + y
2. Simplify both equations as much as possible. We can combine like terms on both sides of the equations:
Equation 1: x - 5y = -7 (subtract x from both sides, subtract 2 from both sides)
Equation 2: 2x - 3y = 5 (add 2y to both sides, add 5 to both sides)
3. Now, we have a system of two linear equations:
- Equation 1: x - 5y = -7
- Equation 2: 2x - 3y = 5
4. There are several methods to solve this system of equations, such as substitution, elimination, or graphing. Let's use the substitution method here.
5. Solve Equation 1 for x:
- x = 5y - 7
6. Substitute this value of x into Equation 2:
- 2(5y - 7) - 3y = 5
- 10y - 14 - 3y = 5
- 7y - 14 = 5
- 7y = 5 + 14
- 7y = 19
- y = 19/7
7. Substitute the value of y back into the equation we found in step 5 to solve for x:
- x = 5(19/7) - 7
- x = 95/7 - 49/7
- x = 46/7
8. So the solution to the system of equations is x = 46/7 and y = 19/7.
Remember, when solving systems of equations, always double-check your solution by plugging the values back into the original equations to ensure they satisfy all the given equations.
I suppose that means
2x-3y+2 = x+2y-5
x+2y-5 = 3x+y
or, rearranging things into a more standard form,
x-5y = -7
2x-y = -5
now, since y = 2x+5,
x-5(2x+5) = -7
-9x-25 = -7
x = -2
so, y = 2*-2 + 5 = 1