Question

solve the system by substitution. check your solution.

$0.5x + 0.25y = 36$

$y + 18 = 16x$

a. $(36, 72)$ \t\t\t\t c. $(49, 81)$
b. $(9, 126)$ \t\t\t\t d. $(21, 9)$

please select the best answer from the choices provided

a
b
c
d

Explanation:

Step1: Isolate y from second equation

$y = 10x - 18$

Step2: Substitute y into first equation

$0.5x + 0.25(10x - 18) = 36$

Step3: Simplify the equation

$0.5x + 2.5x - 4.5 = 36$
$3x = 40.5$
$x = 13.5$? Correction: Wait, recalculate: $0.5x + 2.5x = 3x$, $36 + 4.5 = 40.5$, $x = 40.5 / 3 = 13.5$? No, check substitution again: $0.25*10x=2.5x$, $0.25*(-18)=-4.5$, so $0.5x+2.5x=3x=36+4.5=40.5$, $x=13.5$? No, wait check options: test option b (9,126):
First equation: $0.5*9 +0.25*126=4.5+31.5=36$ (correct). Second equation: $126+18=144=10*14.4$? No, wait original second equation: $y+18=10x$ → $126+18=144=10*14.4$ no. Wait option a (36,72): $72+18=90=10*9≠10*36$. Option c (49,81): $81+18=99≠10*49$. Option d (21,9): $9+18=27≠10*21$. Wait maybe typo in second equation: if it's $y=10x-18$, then for x=9: y=72, check first equation: 0.59+0.2572=4.5+18=22.5≠36. For x=36: y=342, no. Wait wait first equation: 0.5x+0.25y=36 multiply by 4: 2x+y=144. Second equation: y+18=10x → y=10x-18. Substitute into 2x+y=144: 2x+10x-18=144 →12x=162→x=13.5, y=117. Not in options. But the only option that works in[SSE Completed, Client Connection Error][SSE onError error]

Answer:

b. (9, 126)