Final answer:
To solve the given system of equations, express y in terms of x from the first equation and substitute it into the second. Upon solving, it is found that x=0 and y=-3, which is the solution to the system.
Step-by-step explanation:
Solving the System of Equations Using Substitution
To solve the system of equations given, which are:
We start with substitution. First, from the first equation, we can express y in terms of x:
y = 5x - 3
Now, we'll substitute this expression for y into the second equation:
3x - 8(5x - 3) = 24
Expanding the brackets and solving for x gives:
3x - 40x + 24 = 24
-37x = 0
x = 0
Substitute x = 0 back into the first equation to find the value of y:
-5(0) + y = -3
y = -3
Therefore, the solution to the system of equations is x=0 and y=-3. These values satisfy both original equations.
This process involved several algebraic steps and the careful substitution of variables.