Solve the system by substitution.y, equals, minus, xy=−xy, equals, minus, 4, x, plus, 12y=−4x+12

1. Break Down the Problem

We have a system of equations:

1. $y = -x$
2. $y = -4x + 12$

We will solve this system using substitution.

2. Relevant Concepts

In substitution method, we replace one variable with the expression of the other variable from one equation into the other equation.

3. Analysis and Detail

1. Substitute: From equation 1, $y = -x$. We substitute $y$ in equation 2: $-x = -4x + 12$

2. Solve for x: $-x + 4x = 12$ $3x = 12$ $x = 4$

3. Find y: Now we substitute $x = 4$ back into equation 1 to find $y$: $y = -x = -4$

4. Verify and Summarize

We can verify our solution by substituting $x$ and $y$ back into both original equations to check if they hold true.

• For $y = -x$: $-4 = -4 \quad (True)$

• For $y = -4x + 12$: $-4 = -4(4) + 12 \Rightarrow -4 = -16 + 12 = -4 \quad (True)$

Final Answer

The solution to the system of equations is: $\boxed{(4, -4)}$