Question

Which of the following is true about the system 4/3x−2/5y=2 and 3x−2y=−1?

Select one:
a. The system is consistent and independent.
b. The system is inconsistent.
c. The system has infinitely many solutions.
d. The system is consistent and dependent.

Answer 1

Equation 1 is $\frac{4}{3}x -\frac{2}{5}y =2$ ,

Equation 2 is [/tex] 3x-2y = -1 [/tex]

for first equation LCD= 3 *5 = 15 , So we multiply whole equation by 15

$\frac{4}{3} *15x -\frac{2}{5}*15 y =2*15$

$20x - 6y = 30$

Now multiply second equation by -3 , to make the coefficient of y equal and opposite , so that we can apply the elimination method

$-9x+6y = 3$

Add both the equations

$20x -9x -6y +6y = 30+3$

$11x= 33$

Divide both sides by 11

$x=3$

Plug in any one of the equation we get

3(3) -2y = -1

9 - 2y = -1

subtract 9 from both sides

-2y = -10

divide both sides by -2

y=5

So the solution is x= 3 , y= 5

Which means

a. The system is consistent and independent. TRUE