Question

Y = 4x - 9 y equals x minus 3 solve by substitution

Answer 1

To solve the system of equations using substitution, we start with the two equations given:

1. \( Y = 4x - 9 \)
2. \( Y = x - 3 \)

Since both equations are equal to \( Y \), we set them equal to each other:

\[
4x - 9 = x - 3
\]

Now, let's solve for \( x \):

1. Subtract \( x \) from both sides:

\[
4x - x - 9 = -3
\]

This simplifies to:

\[
3x - 9 = -3
\]

2. Next, add 9 to both sides:

\[
3x = 6
\]

3. Divide both sides by 3:

\[
x = 2
\]

Now that we have \( x \), we can substitute it back into one of the original equations to find \( Y \). We'll use the second equation:

\[
Y = x - 3
\]
Substituting \( x = 2 \):

\[
Y = 2 - 3 = -1
\]

Thus, the solution to the system of equations is:

\[
(x, Y) = (2, -1)
\]

So, the solution is \( x = 2 \) and \( Y = -1 \).