Question

solve the following system of linear equations by substitution and determine whether the system has one solution, no solution, or an infinite number of solutions. if the system has one solution, find the solution.
\

$$\begin{cases} 4x + y = 21 \\\\ 8x + 2y = 24 \\end{cases}$$

answer
selecting an option will enable input for any required text boxes. if the selected option does not have any associated text boxes, then no further input is required.
\bigcirc one solution \quad (\quad, \quad)
\bigcirc no solution
\bigcirc infinite number of solutions

Explanation:

Step1: Solve for y from first equation

From \(4x + y = 21\), we get \(y = 21 - 4x\).

Step2: Substitute y into second equation

Substitute \(y = 21 - 4x\) into \(8x + 2y = 24\):
\(8x + 2(21 - 4x) = 24\)

Step3: Simplify the equation

Expand: \(8x + 42 - 8x = 24\)
Simplify: \(42 = 24\), which is false.

Answer:

No Solution