Answer:
[tex]\left(\dfrac{13}9,\ \dfrac{43}{27}\right)[/tex]
Step-by-step explanation:
We can solve the system of equations by elimination:
(eq 1) 5x + 3y = 12
(eq 2) 2x + 12y = 22
[step 1] multiply (eq 1) by 4 to get (eq 3):
4(5x + 3y = 12)
⇒ 20x + 12y = 48 (eq 3)
[step 2] subtract (eq 3) from (eq 2)
(eq 2) 2x + 12y = 22
(eq 3) -(20x + 12y = 48)
-18x + 0 = -26
[step 3] solve for x in the resulting equation
-18x = -26
x = (-26) / (-18)
[tex]\boxed{x=\dfrac{13}{9}}[/tex]
[step 4] plug this x-value into (eq 1) to solve for y
5[tex]\left(\frac{13}9\right)[/tex] + 3y = 12
[tex]\frac{65}9[/tex] + 3y = 12
3y = 12 - [tex]\frac{65}9[/tex]
3y = [tex]\frac{43}9[/tex]
[tex]\boxed{y=\dfrac{43}{27}}[/tex]
[step 5] assemble the x- and y-values into an ordered pair (x, y)
[tex]\left(\dfrac{13}9,\ \dfrac{43}{27}\right)[/tex]
This is the point on the graph where the lines formed by (eq 1) and (eq 2) intersect.
