Question

What is the solution to 5x-8y=-45 9x-8y=49

Answer 1

Answer:

$\large\boxed{x=\dfrac{47}{2},\ y=\dfrac{325}{16}\ or\ x=23.5,\ y=20.3125}$

Step-by-step explanation:

$\left\{\begin{array}{ccc}5x-8y=-45\\9x-8y=49&\text{change all signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}5x-8y=-45\\-9x+8y=-49\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-4x=-94\qquad\text{divide both sides by (-4)}\\\\.\qquad\dfrac{-4x}{-4}=\dfrac{-94}{-4}\\\\.\qquad \boxed{x=\dfrac{47}{2}=23.5}\\\\\text{Put the value of}\ x\ \text{to the first equation}\\\\5(23.5)-8y=-45\\\\117.5-8y=-45\qquad\text{subtract 117.5 from both sides}$

$-8y=-162.5\qquad\text{divide both sides by (-8)}\\\\\dfrac{-8y}{-8}=\dfrac{-162.5}{-8}\\\\y=\dfrac{1625}{80}\\\\\boxed{y=\dfrac{325}{16}=20.3125}$