How do you solve the following system?: $x - 3y = 0 , x = 1/2y + 3$

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How do you solve the following system?: $x - 3y = 0 , x = 1/2y + 3$

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Answer 1 · 2015-12-20T09:01:43

point of intersection $=(18/5,6/5)$

Explanation:

When you solve a system, you are finding the point(s) at which the two lines intersect. We can solve a system by using elimination or substitution. In this case, we will use substitution.

To solve the system, we need to find the values of $x$ and $y$ . First, label your equations.

Equation $1$ : $x-3y=0$
Equation $2$ : $x=1/2y+3$

$1.$ Start by substituting equation $2$ into equation $1$ to solve for $y$ :

$x-3y=0$

$(1/2y+3)-3y=0$

$(1/2y+6/2)-6/2y=0$

$(y+6)/2-6/2y=0$

$(y+6-6y)/2=0$

$-5y+6=0$

$-5y=-6$

$y=6/5$

$2.$ Now that you have the value of $y$ , substitute $y=6/5$ into either equation $1$ or $2$ to find the value of $x$ . In this case, we will substitute it into equation $1$ :

$x-3y=0$

$x-3(6/5)=0$

$x-18/5=0$

$x=18/5$

$:.$ , the point of intersection is $(18/5,6/5)$ .

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How do you solve the following system?: $x - 3y = 0 , x = 1/2y + 3$

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How do you solve the following system?: $x - 3y = 0 , x = 1/2y + 3$