Find a, b∈|r, knowing that the systems {3x+4y=10 and {bx+ay=7 {2ax-b=1 {x-2y=0 are equivalent.

Hi there!

So in a standard-form equation, we know that ax + by = c. Using that, we can determine that a = 3, b = 4, c = 10. Using this, we can plug these values in to an equation to find x and y. Let's use the first equation the first equation to solve for y: 4y = 10 - 3x. Divide both sides by 2 so that we can use the equation: 2y = 5 - 1.5x. Now, substitute into an equation: x - 5 - 1.5x = 0. Simplify and subtract: .5x = 5. Divide both sides by 0.5 to get x = 10. Now plug back into the first equation to solve for y: 30 + 4y = 10. Subtract 30 from both sides: 4y = -20. And lastly, divide: y = -5.

Hope this helps!! :)
If my answer is wrong, please let me know, as I am not completely sure of my answer.

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