Solve by substitution:
8x - 4y =16
y=2x -4
Gee, they kind of gave it away with that second equation
Substitute y from the second equation in the first equation.
8 x - 4 ( 2 x - 4 ) = 16
or
8 x - 8 x + 16 = 16
0 = 0
This is frustrating, but look at why
write that first equation as
4 y = 8 x - 16
divide both sides by 4
y = 2 x - 4
TILT !!! That is exactly the second equation.
To find the intersection of two lines, you need two lines. We only have one here because both equations are he same when reduced to form y = m x + b
So.
There is no solution - sorry about that.
Damon! Thank you! You are very generous with your skill and knowledge. If you have time, would you take a look at some other algrbra problem I need help and understanding with? Unlike some others, you have been most thourough in explaining the process. Thank you, Carl.
To solve this system of equations by substitution, we will substitute the value of y from the second equation into the first equation.
Given equations:
8x - 4y = 16 ...(Equation 1)
y = 2x - 4 ...(Equation 2)
To substitute the value of y from Equation 2 into Equation 1, we replace y with 2x - 4 in Equation 1:
8x - 4(2x - 4) = 16
Now, simplify and solve for x:
8x - 8x + 16 = 16 (distributing the negative sign to both terms inside the parentheses)
16 = 16 (simplifying)
The equation simplifies to 16 = 16, which is always true. This means that the two equations are dependent (represent the same line) and have infinitely many solutions.
Thus, the solution to the system of equations is all values of x and y that satisfy the equation y = 2x - 4.