Question

Solve the following system of equations using substitution:

-5x + y = -3
3x - 8y = 24

Answer 1

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:

• -5x + y = -3
• 3x - 8y = 24

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.