Question

5x + 3y = 16
3x -5y = -4
How do I solve this

Answer 1

`(2, 2)`

Explanation:

We can solve this system of equations using the elimination method.

Let's start by multiplying the first equation by 3:

`3(5x+3y)=3(16)\\3(5x)+3(3y)=48\\15x+9y=48`

Now, multiply the second equation by 5:

`5(3x-5y)=5(-4)\\5(3x)-5(5y)=-20\\15x-25y=-20`

Since both equations have 15x, we can eliminate the x by subtracting the two equations.

`15x-15x+9y-(-25y)=48-(-20)\\9y+25y=68\\34y=68\\\text{Divide both sides by 34}\\y=2`

Now, substitute 2 for y to solve for x:

`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`

Therefore the solution to this system of equations is:

`(x, y)=(2, 2)`