If y=2x+2 and 4x+3y=26m, then find the value of x^2+y^2

x² + y² is equal to = (4 / 81)(845m² + 78m + 18)

Step-by-step explanation:

We first need to get the values of x and y, which can be done using a system of equations, substituting one of the two functions into the other:

Given:

y = 2x + 2

3x + 3y = 26m

Then:

3x + 3(2x + 2) = 26m

3x + 6x + 6 = 26m

9x + 6 = 26m

9x = 26m - 6

x = (26m - 6) / 9

Now we can solve for y:

y = 2x + 2

y = 2(26m - 6) / 9 + 2

y = 2(26m - 6) / 9 + 18 / 9

y = (52m - 12 + 18) / 9

y = (52m + 6) / 9

Now we can sum up their squares:

x² + y²

= ((26m - 6) / 9)² + ((52m + 6) / 9)²

= (676m² - 312m + 36) / 81 + (2704m² + 624m + 36) / 81

= (3380m² + 312m + 72) / 81

= (4 / 81)(845m² + 78m + 18)

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step-by-step explanation: