Final answer:
To solve the given system of linear equations by substitution, solve one equation for a variable and substitute it into the other equation. We find that x = 5 and y = -1.
Step-by-step explanation:
To solve linear equations by substitution, one of the equations can be solved for one variable, which then can be substituted into the other equation. Given the equations 4x-3y=23 and x+4y=1, we can solve the second equation for x:
x = 1 - 4y
Now, we substitute this expression for x into the first equation:
4(1 - 4y) - 3y = 23
This simplifies to:
4 - 16y - 3y = 23
Combining like terms, we get:
-19y = 19
Dividing both sides by -19, we get:
y = -1
Substitute this value back into the equation for x:
x = 1 - 4(-1)
x = 1 + 4
x = 5
Therefore, the solution to the system of equations is x = 5 and y = -1.