Question

Show that (2, 1) is a solution of the system of equations.

x + 3y = 5,

y = –x + 3

Substitute (2, 1) into x + 3y = 5 to get
.
Simplify the equation to get
.
Substitute (2, 1) into y = –x + 3 to get
.
Simplify the equation to get
.

Answer 1

To verify that (2, 1) is a solution of the system of equations, we will substitute \(x = 2\) and \(y = 1\) into each equation and simplify.

1. **Substituting into the first equation:**

The first equation is:
\[
x + 3y = 5
\]
Substitute \(x = 2\) and \(y = 1\):
\[
2 + 3(1) = 5
\]
Now simplify:
\[
2 + 3 = 5
\]
\[
5 = 5
\]
This is true, so (2, 1) is a solution to the first equation.

2. **Substituting into the second equation:**

The second equation is:
\[
y = -x + 3
\]
Substitute \(x = 2\) and \(y = 1\):
\[
1 = -2 + 3
\]
Now simplify:
\[
1 = 1
\]
This is also true, so (2, 1) is a solution to the second equation as well.

Since (2, 1) satisfies both equations, we conclude that (2, 1) is indeed a solution of the system of equations.