Question

Please I really need help 100 points

What is the solution to the system of equations?

Use any method.

{2x−3y=9 3x+5y=4

Answer 1

x = 3 and y = -1 ⇒ (3, -1)

Explanation:

`\left\{\begin{array}{ccc}2x-3y=9&\text{multiply both sides by 5}\\3x+5y=4&\text{multiply both sides by 3}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}10x-15y=45\\9x+15y=12\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad19x=57\qquad\text{divide both sides by 19}\\.\qquad x=3\\\\\text{Put the value of x to the second equation:}\\\\3(3)+5y=4\\9+5y=4\qquad\text{subtract 9 from both sides}\\5y=-5\qquad\text{divide both sides by 5}\\y=-1`

Answer 2

Multiply the first equation by 3 and the second equation by 2:

`\begin{cases}6x-9y=27\\6x+10y=8\end{cases}`

Subtract the two equation to get rid of the x variable:

`-9y-10y=27-8 \iff -19y = 19 \iff y = -1`

Use the value of y to determine the value of x: for example, using the first equation we have

`2x+3=9 \iff 2x=6 \iff x=3`