Question

Question #2077b

Answer 1

Answer: `(7/2,1)`

Explanation:

Solve:
`2x+3y=10`
`5x+2y=19.5`

We can solve this system of equations by elimination.
First, we need to multiply the first equation by `5` and the second equation by `2` to make the `x` coefficient same for both equations:
`5(2x+3y=10)`
`10x+15y=50`

`2(5x+2y=19.5)`
`10x+4y=39`

Since the `x` coefficient for both equations is now `10`, we can subtract the second equation from the first equation and simplify:
`10x+15y-(10x+4y)=50-39`
`10x+15y-10x-4y=11`
`11y=11`
`y=1`

Now, we can substitute this `y` value into one of the original equations and solve for `x`, we'll use the first one:
`2x+3(1)=10`
`2x+3=10`
`2x=7`
`x=7/2`

Therefore, our answer as a coordinate is `(7/2,1)`