What is the solution of the system of equations below?
\[
\begin{align*}
2x + 3y &= 7 \\
x + y &= 3 \\
\end{align*}
\]
Options:
1. (1, 2)
2. (2, 1)
3. (4, -1)
4. (4, 1)
Answer (3)
{ 2 x + 3 y = 7 x + y = 3 / ∗ ( − 2 ) { 2 x + 3 y = 7 − 2 x − 2 y = − 6 + − − − − − − − y = 1 2 x + 3 ⋅ 1 = 7
2 x + 3 = 7 ∣ − 3 2 x + 3 − 3 = 7 − 3 2 x = 4 / : 2 x = 2 { x = 2 y = 1
2x + 3y = 7 x + y = 3
x = 3 - y
substituting for x,
2(3 - y) + 3y = 7
= 6 - 2y + 3y = 7 6 + y = 7
thus, y = 1
x = 3 - y
= 3 - 1 = 2.
Thus, x = 2 , y = 1
Thus, (2) is correct.
The solution to the system of equations is (x, y) = (2, 1). The method used was substitution, starting from the second equation. This leads us directly to the values of x and y that solve both equations.
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