Question

Could someone help please!! Will give brainliest!

Answer 1

The answer is x = 1/2 y = 2.

Using substitution means plugging in a different value. In this system, y has a value in x form and there is another equation.

To find the variables, first plug in y in x form to second equation to solve for x:
$x + \frac{1}{3} ( - 3x + 4) = \frac{4}{3}$
Remove the parentheses and set the denominators equal:
$\frac{x}{3} + \frac{- 9x + 12}{3} = \frac{4}{3}$
Combine left side:
$\frac{x( - 9x + 12)}{3} = \frac{4}{3}$
Remove the denominators and simplify:
$- 9 {x}^{2} + 12x = 4$
Turn the equation into standard form:
$9 {x}^{2} - 12x + 4 = 0$
Factor it as a perfect square trinomial:
$(3x - 2) \times (3x - 2)$
To solve for x:
$3x - 2 = 0 \\ \\ 3x = 2 \\ \\ x = \frac{2}{3}$
So if x is 2/3, we can plug that in the first equation to find y:
$y = - 3 \times \frac{2}{3} + 4$
Simplify:
$y = \frac{ - 3 \times 2}{3} + \frac{12}{3} \\ \\ y = \frac{ - 6}{3} + \frac{12}{3} \\ \\ y = \frac{12 - 6}{3} = \frac{6}{3} = 2$
So y is equal to 2.