1 Answer

Derekaug · Answer 1 · 2021-03-25T03:16:15+0000

What ordered pair represents the solution to this system of linear equations?

3y = 2x + 2

y = 4/3x + 1

Options

(−1/2, 1/3)

(−1/3, 1/2)

(1/3, −1/2)

(1/2, −1/3)

The ordered pair that represents the solution to the given system of linear equations is
((-1)/(2) , (1)/(3))

Given system of linear equations are:

3y = 2x + 2 ---- eqn 1

y = (4)/(3)x + 1 --- eqn 2

Let us solve the given system of equations to find the ordered pair (x, y)

Substitute eqn 2 in eqn 1

$3((4)/(3)x + 1)=2x + 2\\\\4x + 3 = 2x + 2\\\\4x - 2x = 2 - 3\\\\2x = -1\\\\x = (-1)/(2)$

$\text{ Substitute }x = (-1)/(2) \text{ in eqn 2 }$

$y = (4)/(3) * (-1)/(2) + 1\\\\y = (-2)/(3) + 1\\\\y = (-2+3)/(3)\\\\y = (1)/(3)$

Thus the ordered pair that represents the solution to the given system of linear equations is
((-1)/(2) , (1)/(3))

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