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.$\begin{cases}4x + y = 23 \\-4x + 2y = -26end{cases}$answerselecting 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.$circ$ one solution ( )$\bullet$ no solution$circ$ infinite number of solutions

Explanation:

Step1: Isolate y from first equation

$y = 23 - 4x$

Step2: Substitute y into second equation

$-4x + 2(23 - 4x) = -26$

Step3: Simplify and solve for x

$-4x + 46 - 8x = -26$
$-12x + 46 = -26$
$-12x = -26 - 46$
$-12x = -72$
$x = \frac{-72}{-12} = 6$

Step4: Substitute x to find y

$y = 23 - 4(6) = 23 - 24 = -1$

Step5: Verify solution in both equations

Check $4(6) + (-1) = 24 - 1 = 23$ (matches first equation)
Check $-4(6) + 2(-1) = -24 - 2 = -26$ (matches second equation)

Answer:

One Solution
$(6, -1)$