Solve the system by substitution.
-5x + y = -3
3x - 8y = 24
I'm not sure which equation to choose as I begin to find the y value. Some assistance would be greatly appreciated! Thank you!
in your first equation the coefficient of y is 1, so that becomes your obvious choice.
y = 5x - 3
sub that into the 2nd
3x - 8(5x-3) = 24
3x - 40x + 24 = 24
-37x = 0
x = 0
back into y = 5x-3
y = 0 - 3 = -3
x = 0 , y = -3
Thank. You. So. Much
To solve the system by substitution, we can choose either equation to begin with.
Let's solve the first equation for y:
-5x + y = -3
Rearranging this equation to isolate y, we have:
y = 5x - 3
Now we can substitute this expression for y into the second equation:
3x - 8(5x - 3) = 24
Simplify the equation:
3x - 40x + 24 = 24
Combine like terms:
-37x + 24 = 24
Subtract 24 from both sides:
-37x = 0
Divide both sides by -37:
x = 0
Now we can substitute this value of x back into the equation we used to solve for y:
y = 5(0) - 3
y = -3
Therefore, the solution to the system of equations is x = 0 and y = -3.
To solve the system by substitution, you choose one equation and solve it for either variable. Then, you substitute the value you found into the other equation to solve for the remaining variable.
Let's start by solving the first equation for y:
-5x + y = -3
To isolate y, we can add 5x to both sides:
y = 5x - 3
Now that we have an expression for y, we can substitute it into the second equation:
3x - 8(5x - 3) = 24
First, distribute the -8:
3x - 40x + 24 = 24
Combine like terms:
-37x + 24 = 24
Next, subtract 24 from both sides:
-37x = 0
Divide by -37:
x = 0
Now that we have the value for x, we can substitute it back into the first equation to find y:
-5(0) + y = -3
Simplify:
y = -3
Therefore, the solution to the system is x = 0 and y = -3.