Answer:
Explanation:
1. One way to use substitution to solve this problem is to substitute the expression for Y from the second equation into the first equation. This gives:
X = 3Y - 7
X = 3(X + 1) - 7
We can simplify the second equation by distributing the 3:
X = 3X + 3 - 7
Then we can combine like terms:
X - 3X = -4
Solving for X, we get:
-2X = -4
X = 2
Now we can substitute this value for X into either equation to solve for Y. Using the second equation:
Y = X + 1
Y = 2 + 1
Y = 3
So the solution to the system of equations is X = 2 and Y = 3.
2. Substituting 3X - 7 for X in the first equation, we get:
X = 3Y - 7
(3X - 7) = 3Y - 7
We can simplify by adding 7 to both sides:
3X = 3Y
Then we can divide both sides by 3:
X = Y
Now we can substitute this expression for X into either equation to solve for Y. Using the second equation:
Y = X + 1
Y = Y + 1
Subtracting Y from both sides, we get:
0 = 1
This is a contradiction, so there is no solution to the system of equations when we substitute 3X - 7 for X.
3. To find the solutions to the system of equations:
X = 3Y - 7 (equation 1)
Y = X + 1 (equation 2)
We can use substitution. From equation 2, we can express X in terms of Y:
X = Y - 1
Substituting this into equation 1, we get:
Y - 1 = 3Y - 7
Simplifying the equation, we get:
2Y = 6
Dividing both sides by 2, we get:
Y = 3
Now we can substitute this value for Y into either equation to solve for X. Using equation 2:
Y = X + 1
3 = X + 1
Subtracting 1 from both sides, we get:
X = 2
Therefore, the solution to the system of equations is X = 2 and Y = 3.