Final answer:
By solving the first equation for y and substituting into the second equation, we find x = 11 and y = 14. Substituting these values back into the original equations confirms that (11, 14) is the correct solution to the system of linear equations.
Step-by-step explanation:
To solve the system of linear equations by substitution, we start with the given equations −x + y = 3 and 3x − 2y = 5. We first solve one of the equations for one variable and then substitute that expression into the other equation.
From the first equation, −x + y = 3, solve for y:
y = x + 3
Now substitute the expression for y into the second equation, 3x − 2y = 5:
3x − 2(x + 3) = 5
Expand and solve for x:
3x − 2x − 6 = 5
x − 6 = 5
x = 11
Now that we have found x, we substitute it back into the expression for y:
y = 11 + 3
y = 14
The solution to the system is (x, y) = (11, 14).
To check the solution, substitute the values back into the original equations:
−(11) + 14 = 3 (True)
3(11) − 2(14) = 5 (True)
Since both statements are true, (11, 14) is indeed the solution to the system of equations.