Question

solve with substitution and within an ordered pair;
2x-3y=19
y=x-7

Answer 1

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:

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