Question

Solve the system of equations. \begin{aligned} & -5y-10x = 45 \\\\ &-3y+10x=-5 \end{aligned} ​ −5y−10x=45 −3y+10x=−5 ​

Answer 1

`\boxed{\sf \ \ \ x=-2 \ \ \ and \ \ \ y=-5 \ \ \ }`

Explanation:

let s solve the following system

(1) -5y-10x=45

(2) -3y+10x=-5

let s do (1) + (2) it comes

-5y-10x-3y+10x=45-5=40

<=>

-8y=40

<=>

y = -40/8=-20/4=-5

so y = -5

let s replace y in (1)

25-10x=45

<=>

10x=25-45=-20

<=>

x = -20/10=-2

so x = -2

Answer 2

x = -2

y = -5

Explanation:

We can solve this algebraically (substitution or elimination) or graphically. I will be using elimination:

Step 1: Add the 2 equations together

-8y = 40

y = -5

Step 2: Plug y into an original equation to find x

-3(-5) + 10x = -5

15 + 10x = -5

10x = -20

x = -2

And we have our final answers!