Question

question 10 of 14, step 1 of 1
solve the following system of linear equations by addition. indicate whether the given system of linear equations has one solution, has no solution, or has an infinite number of solutions. if the system has one solution, find the solution.
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$$\begin{cases} 4x + y = 13 \\\\ 8x + 2y = 26 \\end{cases}$$

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answer
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$\bigcirc$ one solution $\quad (\quad, \quad)$
$\bigcirc$ no solution
$\bigcirc$ infinite number of solutions

Explanation:

Step1: Scale first equation by 2

Multiply $4x + y = 13$ by 2:
$$2(4x + y) = 2(13)$$
$$8x + 2y = 26$$

Step2: Compare scaled and second equation

The scaled first equation is identical to the second equation $8x + 2y = 26$. This means the two equations represent the same line, so every point on the line is a solution.

Answer:

Infinite Number of Solutions