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Solve the System of Linear Equations: x + y = 10 and 2x - y = 2
Published on April 12, 2025
Algebra
Solve the given system of linear equations by using the elimination method to find the values of x and y.
Question
Solve the system of equations: x + y = 10 2x - y = 2
Answer
To solve the system of equations:
we can use the method of substitution or elimination. Here, we’ll use the elimination method.
- Add the two equations to eliminate
:
- Solve for
:
- Substitute
back into the first equation to solve for :
Thus, the solution to the system of equations is:
## Solution to the System of Equations
To solve the system of equations:
$$
\begin{cases}
x + y = 10 \\
2x - y = 2
\end{cases}
$$
we can use the method of substitution or elimination. Here, we'll use the elimination method.
1. **Add the two equations to eliminate \( y \):**
$$
(x + y) + (2x - y) = 10 + 2
$$
$$
x + y + 2x - y = 12
$$
$$
3x = 12
$$
2. **Solve for \( x \):**
$$
x = \frac{12}{3} = 4
$$
3. **Substitute \( x = 4 \) back into the first equation to solve for \( y \):**
$$
x + y = 10
$$
$$
4 + y = 10
$$
$$
y = 10 - 4
$$
$$
y = 6
$$
Thus, the solution to the system of equations is:
$$
(x, y) = (4, 6)