Solve the system by substitution.y, equals, minus, 7, xy=−7xy, equals, minus, 5, x, plus, 10y=−5x+10

1. Break Down the Problem

We are given a system of equations to solve by substitution. The two equations are:

1. $y = -7$
2. $xy = -5x + 10$

We will substitute the expression for $y$ from the first equation into the second equation.

2. Relevant Concepts

To solve for $x$ using substitution, we will replace $y$ in the second equation with $-7$.

3. Analysis and Detail

1. Substitute $y = -7$ into the second equation: $x(-7) = -5x + 10$ This simplifies to: $-7x = -5x + 10$

2. Rearranging the equation to isolate $x$: $-7x + 5x = 10$ $-2x = 10$ Dividing both sides by -2: $x = -5$

4. Verify and Summarize

Now that we have $x = -5$, we can find $y$ using the first equation: $y = -7$

Final Answer

The solution to the system is $x = -5$ and $y = -7$.