Question

Solve the system by substitution.
minus, 5, x, minus, 6, y, equals, 7
−5x−6y=
7
x, equals, minus, y
x=
−y

Answer 1

Solve the system by substitution.
x, equals, y
x=
y
minus, 3, x, minus, y, equals, 4
−3x−y=
4

Answer 2

To solve the system of equations using substitution, we have the following equations:

1. \(-5x - 6y = 7\)
2. \(x = -y\)

We'll substitute the second equation into the first equation.

Substituting \(x = -y\) into \(-5x - 6y = 7\):

\[
-5(-y) - 6y = 7
\]

This simplifies to:

\[
5y - 6y = 7
\]

Combine like terms:

\[
-y = 7
\]

To find \(y\), we multiply both sides by -1:

\[
y = -7
\]

Now that we have \(y\), we can use the second equation to find \(x\):

\[
x = -y
\]

Substituting \(y = -7\):

\[
x = -(-7) = 7
\]

The solution to the system is:

\[
x = 7,\ y = -7
\]

So the solution to the system of equations is:

\[
(x, y) = (7, -7)
\]

Answer 3

To solve the system of equations using substitution, we have the following equations:

1. \(x = y\)
2. \(-3x - y = 4\)

We will substitute the first equation into the second equation.

Substituting \(x = y\) into \(-3x - y = 4\):

\[
-3(y) - y = 4
\]

This simplifies to:

\[
-3y - y = 4
\]

Combining like terms gives us:

\[
-4y = 4
\]

Now, divide both sides by -4:

\[
y = -1
\]

Now that we have \(y\), we can use the first equation to find \(x\):

\[
x = y
\]

Substituting \(y = -1\):

\[
x = -1
\]

The solution to the system is:

\[
x = -1, \quad y = -1
\]

So the solution to the system of equations is:

\[
(x, y) = (-1, -1)
\]