Answer:
[tex](7,\frac{13}{3})[/tex]
Step-by-step explanation:
we have
The equation of the first line
[tex]y=\frac{1}{3}x+2[/tex] ------> equation A
The equation of the second line
[tex]y=\frac{4}{3}x-5[/tex] ------> equation B
Solve the system of equations by elimination
Multiply equation A by -4 both sides
[tex](-4)y=(-4)(\frac{1}{3}x+2)[/tex]
[tex]-4y=-\frac{4}{3}x-8[/tex] --------> equation C
Adds equation B and equation C
[tex]y=\frac{4}{3}x-5\\-4y=-\frac{4}{3}x-8\\--------\\y-4y=-5-8\\-3y=-13\\y=\frac{13}{3}[/tex]
Find the value of x
substitute the value of y
[tex]\frac{13}{3}=\frac{1}{3}x+2[/tex]
[tex]\frac{1}{3}x=\frac{13}{3}-2[/tex]
Multiply by 3 both sides
[tex]x=13-6[/tex]
[tex]x=7[/tex]
therefore
The solution to the system of equations is the point [tex](7,\frac{13}{3})[/tex]
