7. Systems of Equations & Matrices

Two Variable Systems of Linear Equations

7. Systems of Equations & Matrices

Two Variable Systems of Linear Equations

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Multiple Choice

Solve the following system of equations. Classify it as CONSISTENT (INDEPENDENT or DEPENDENT) or INCONSISTENT.
$2x+8y=7$
$x+4y=19$

Consistent and Independent

Consistent and Dependent

Inconsistent

Verified step by step guidance

Step 1: Start by writing down the given system of equations. The first equation is $2x + 8y = 7$ and the second equation is $x + 4y = 19$.

Step 2: To solve the system, we can use the method of elimination. First, multiply the second equation by 2 to align the coefficients of $x$ in both equations. This gives us $2x + 8y = 38$.

Step 3: Now, subtract the first equation $2x + 8y = 7$ from the modified second equation $2x + 8y = 38$. This will eliminate $x$ and $y$ terms, resulting in $0 = 31$.

Step 4: The equation $0 = 31$ is a contradiction, indicating that there is no solution to the system of equations. This means the system is inconsistent.

Step 5: Since the system is inconsistent, it does not have any solutions, and therefore cannot be classified as consistent (independent or dependent).