Question

1. solve using substitution:

2x - 3y = -1
y = x - 1
solution: ____________.

Explanation:

Step1: Substitute \( y = x - 1 \) into \( 2x - 3y = -1 \)

We replace \( y \) in the first equation with \( x - 1 \) (since \( y = x - 1 \) from the second equation). So the first equation becomes:
\( 2x - 3(x - 1) = -1 \)

Step2: Simplify and solve for \( x \)

First, distribute the -3 in \( -3(x - 1) \):
\( 2x - 3x + 3 = -1 \)
Combine like terms (\( 2x - 3x = -x \)):
\( -x + 3 = -1 \)
Subtract 3 from both sides:
\( -x = -1 - 3 \)
\( -x = -4 \)
Multiply both sides by -1 to solve for \( x \):
\( x = 4 \)

Step3: Substitute \( x = 4 \) into \( y = x - 1 \) to find \( y \)

Now that we know \( x = 4 \), we plug this value into the equation \( y = x - 1 \):
\( y = 4 - 1 \)
\( y = 3 \)

Answer:

The solution to the system of equations is \( x = 4 \) and \( y = 3 \), or as an ordered pair \( (4, 3) \)