Question

3х + Зу = -x+5y ordered pair

Answer 1

2x-y=0

x=1/2y

Explanation:

Answer 2

Your solution is (1/2, 1).

Explanation:

3х + Зу = -x + 5y

First we want to look at each side of the equation separately.

3х + Зу ⇒ This expression is fully simplified because you cannot add different variables together.

-x + 5y ⇒ This expression is fully simplified because you cannot add different variables together.

3х + Зу = -x + 5y

Now, let's bring the like terms together.

[add x to both sides]

x + 3x + 3y = -x + x + 5y

4x + 3y = 5y

[subtract 3y from both sides]

4x + 3y - 3y = 5y - 3y

4x = 2y

We want to solve for one variable at a time, so let's isolate x.

[divide both sides by 4]

4x/4 = 2y/4

x = 1/2y

Now we have an expression for x. Plug this expression in to your original equation.

3х + Зу = -x + 5y

3(1/2y) + 3y = -(1/2y) + 5y

According to PEMDAS (parentheses/exponents | multiplication/division | addition/subtraction), we should multiply first.

3(1/2y) + 3y = -(1/2y) + 5y

3/2y + 3y = -1/2y + 5y

Now let's add on each side.

9/2y = 9/2

Now we need to isolate y by dividing both sides by 9/2 (or multiplying by its reciprocal 2/9 ← This is often easier to understand when written)

`(2)/(9) ((9)/(2) y) = (9)/(2) ((2)/(9) )`

In this form, we can see that the fractions cancel each other out.

y = 1

Now that we have the value of y, plug it into our equation for x.

x = 1/2y

x = 1/2(1)

Multiply.

x = 1/2

Your solution is (1/2, 1).

You're almost done! Check your answer by plugging in both these values in to your original equation.

3х + Зу = -x + 5y

3(1/2) + 3(1) = -(1/2) + 5(1)

Multiply.

3(1/2) + 3(1) = -(1/2) + 5(1)

3/2 + 3 = -1/2 + 5

Add.

9/2 = 9/2

This equation is true, therefore your answer is correct!

Hope this helps!