Answer:
Your solution is (1/2, 1).
Step-by-step 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)
[tex]\frac{2}{9} (\frac{9}{2} y) = \frac{9}{2} (\frac{2}{9} )[/tex]
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!
