Question

Find x and y using subsitution -3x + y = 6 5x + 2y =23

Answer 1

$\left\{\begin{array}{ccc}-3x+y=6&|\text{add 3x to both sides}\\5x+2y=23\end{array}\right\\\\\left\{\begin{array}{ccc}y=3x+6\\5x+2y=23\end{array}\right\\\\\text{substitute}\ y=3x+6\ \text{to the second equation}\\\\5x+2(3x+6)=23\qquad|\text{use distributive property}\\\\5x+(2)(3x)+(2)(6)=23\\\\5x+6x+12=23\qquad|\text{subtract 12 from both sides}\\\\11x=11\qquad|\text{divide both sides by 11}\\\\\boxed{x=1}\\\\\text{subtract the value of x to the first equation}\\\\y=3(1)+6\\\\y=3+6\\\\\boxed{y=9}$

Answer: x = 1 and y = 9 → (1, 9).

Answer 2

5x+2y=23
-3x+y=6
-
—————-
8x+y=17
-3x+y=6
-
——————
11x=11
X=1


5+2y=23
2y = 18
Y= 9