Question:
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)
Answer:
The ordered pair that represents the solution to the given system of linear equations is [tex](\frac{-1}{2} , \frac{1}{3})[/tex]
Solution:
Given system of linear equations are:
3y = 2x + 2 ---- eqn 1
[tex]y = \frac{4}{3}x + 1[/tex] --- eqn 2
Let us solve the given system of equations to find the ordered pair (x, y)
Substitute eqn 2 in eqn 1
[tex]3(\frac{4}{3}x + 1)=2x + 2\\\\4x + 3 = 2x + 2\\\\4x - 2x = 2 - 3\\\\2x = -1\\\\x = \frac{-1}{2}[/tex]
[tex]\text{ Substitute }x = \frac{-1}{2} \text{ in eqn 2 }[/tex]
[tex]y = \frac{4}{3} \times \frac{-1}{2} + 1\\\\y = \frac{-2}{3} + 1\\\\y = \frac{-2+3}{3}\\\\y = \frac{1}{3}[/tex]
Thus the ordered pair that represents the solution to the given system of linear equations is [tex](\frac{-1}{2} , \frac{1}{3})[/tex]
