136k views
3 votes
It would be awesome if u could help me!its about solving systems of equations.

It would be awesome if u could help me!its about solving systems of equations.-example-1
User Azucena
by
4.2k points

1 Answer

6 votes

Problem:

Let's denote the above equation like this:

x-3y = -12 EQUATION 1

2x + y = 11 EQUATION 2

Solve x from equation 2:

2x = 11-y

this is equivalent to say (EQUATION 3)


x\text{ = }(11-y)/(2)

Now, replace the variable x in equation 1, that is:


(\text{ }(11-y)/(2))-\text{ 3y = -12}

this is equivalent to say:


(11)/(2)-(y)/(2)-\text{ 3y = -12}

Putting together similar terms on different sides of the equation we get:


(y)/(2)+\text{ 3y = }(11)/(2)+12

this is equivalent to:


\frac{y\text{ + 6y}}{2}\text{= }\frac{11+\text{ 24}}{2}

this is equivalent to:


\frac{7\text{y}}{2}\text{= }(35)/(2)

this is equivalent to:


7\text{y = 35}

solve for y:


y\text{ = }(35)/(7)\text{ = 5}

then, we can conclude that y = 5. But, from lines back we know that x is equal to (EQUATION 3):


x\text{ = }(11-y)/(2)

Replacing y in the previous equation, we obtain


x\text{ = }(11-y)/(2)\text{ = }(11-5)/(2)=\text{ }(6)/(2)\text{ = 3}

then, we can conclude that:

X = 3

Y = 5

It would be awesome if u could help me!its about solving systems of equations.-example-1
User Hanuman
by
3.8k points