Question

Solve using the substitution method
2x+y=5
y=x-4

Answer 1

To solve the system of equations using the substitution method, we can substitute the expression for \(y\) from the second equation into the first equation.

The equations are:

1. \(2x + y = 5\)
2. \(y = x - 4\)

Let's substitute \(y\) from the second equation into the first equation:

\[
2x + (x - 4) = 5
\]

Now, simplify the equation:

\[
2x + x - 4 = 5
\]

Combine like terms:

\[
3x - 4 = 5
\]

Add 4 to both sides:

\[
3x = 9
\]

Now, divide by 3:

\[
x = 3
\]

Now that we have the value of \(x\), we can substitute it back into the second equation to find \(y\):

\[
y = x - 4
\]
\[
y = 3 - 4
\]
\[
y = -1
\]

So the solution to the system of equations is:

\[
(x, y) = (3, -1)
\]

Let's verify the solution by plugging \(x\) and \(y\) back into the first equation:

\[
2(3) + (-1) = 6 - 1 = 5
\]

The first equation holds true, and we have confirmed that our solution is correct.

The final solution is:

\[
(x, y) = (3, -1)
\]