Questions: 4x + 2y = 4 6x - y = 8

Transcript text: $\begin{aligned} 4 x+2 y & =4 \\ 6 x-y & =8\end{aligned}$

Solution

Solution Steps

Step 1: Formulate the Equations in Matrix Form

The system of equations can be represented in matrix form as $Ax = B$, where $A = \begin{pmatrix}4 & 2 \\ 6 & -1\end{pmatrix}$ and $B = \begin{pmatrix}4 \\ 8\end{pmatrix}$.

Step 2: Check the Determinant of A

The determinant of matrix A is $det(A) = -16.0$. Since $det(A) \neq 0$, the system has a unique solution.

Step 3: Apply Cramer's Rule

Using Cramer's Rule, we calculate the determinants $det(A1) = -20.0$ and $det(A2) = 8.0$. Thus, the solution is $x = 1$ and $y = -0$, rounded to 0 decimal places.

Final Answer:

The solution to the system of equations is $x = 1$, $y = -0$.

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