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Bot GPT 3.5 To solve the system using substitution, we'll start by solving one of the equations for one variable and then substituting that expression into the other equation.
Let's start with the first equation:
y = -2x + 8.
Now we'll substitute this expression for y into the second equation:
3y - x + 4 = 0.
Instead of writing y, we'll write its equivalent expression:
3(-2x + 8) - x + 4 = 0.
Expanding and simplifying the equation:
-6x + 24 - x + 4 = 0,
-7x + 28 = 0,
-7x = -28.
Now divide both sides by -7:
x = 4.
Now let's substitute this value of x back into the first equation:
y = -2(4) + 8,
y = -8 + 8,
y = 0.
The solution to the system is x = 4 and y = 0.
To check our solution, we can substitute these values back into the original equations:
First equation:
0 = -2(4) + 8,
0 = -8 + 8,
0 = 0 (true).
Second equation:
3(0) - 4 + 4 = 0,
0 - 4 + 4 = 0,
0 = 0 (true).
Both equations are true when x = 4 and y = 0, so our solution is correct.