Question

Find the solution to the following system of equations:

LaTeX: x+8y=28
x
+
8
y
=
28

LaTeX: -3x+5y=3

Answer 1

x = 14, y = 3 → (14, 3)

Explanation:

`\left\{\begin{array}{ccc}x+8y=28&\text{multiply both sides by 3}\\-3x+5y=3\end{array}\right\\\underline{+\left\{\begin{array}{ccc}3x+24y=84\\-3x+5y=3\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad29y=87\qquad\text{divide both sides by 29}\\\\.\qquad\qquad(29x)/(29)=(87)/(29)\\\\.\qquad\qquad \boxed{y=3}\\\\\text{Put the value of}\ y\ \text{to the first equation:}\\\\x+8(3)=38\\x+24=38\qquad\text{subtract 24 from both sides}\\x+24-24=38-24\\\boxed{x=14}`