solve with substitution and within an ordered pair;

2x-3y=19
y=x-7

1 answer

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

  1. \( 2x - 3y = 19 \)
  2. \( y = x - 7 \)

First, we can substitute \( y \) from the second equation into the first equation:

\[ 2x - 3(x - 7) = 19 \]

Now, distribute \( -3 \):

\[ 2x - 3x + 21 = 19 \]

Combine like terms:

\[ -x + 21 = 19 \]

Now, isolate \( x \) by subtracting 21 from both sides:

\[ -x = 19 - 21 \]

\[ -x = -2 \]

Multiply both sides by -1:

\[ x = 2 \]

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

\[ y = x - 7 \]

\[ y = 2 - 7 \]

\[ y = -5 \]

Now we have both values. The solution to the system of equations, represented as an ordered pair \( (x, y) \), is:

\[ \boxed{(2, -5)} \]