Answer:
[tex](2, 2)[/tex]
Step-by-step explanation:
We can solve this system of equations using the elimination method.
Let's start by multiplying the first equation by 3:
[tex]3(5x+3y)=3(16)\\3(5x)+3(3y)=48\\15x+9y=48[/tex]
Now, multiply the second equation by 5:
[tex]5(3x-5y)=5(-4)\\5(3x)-5(5y)=-20\\15x-25y=-20[/tex]
Since both equations have 15x, we can eliminate the x by subtracting the two equations.
[tex]15x-15x+9y-(-25y)=48-(-20)\\9y+25y=68\\34y=68\\\text{Divide both sides by 34}\\y=2[/tex]
Now, substitute 2 for y to solve for x:
[tex]5x+3y=16\\5x+3(2)=16\\5x+6=16\\\text{Subtract 6 from both sides}\\5x=10\\\text{Divide both sides by 2}\\x=2[/tex]
Therefore the solution to this system of equations is:
[tex](x, y)=(2, 2)[/tex]
