Question

HEEEEELP!!!!!!!!!!!!!11 I WILL MARK BRAINLIEST kx-3y=4 4x-5y=7 k is constant and x and y are variables, for what value of k will the system of equations have NO SOLUTION??? A. 12/5 B. 16/7 C. -16/7 D. -12/5 also side question, how do you find out if an equation has 1 solution or no solution or infinite solutions???

Answer 1

Answer:

              A.  ¹²/₅

Step-by-step explanation:

There is no solution for system of equations:  $a_1x+b_1y=c_1\\a_2y+b_2y=c_2$

if:     $a_1=a_2\quad and\quad b_1=b_2\quad and\quad \bold{c_1\ne c_2}$

so first, we we need to transform the equations to the form where the coefficients at y will be the same:

$kx-3y=4\\ 4x-5y=7\\\\ (kx-3y)\cdot5=4\cdot5\\ (4x-5y)\cdot3=7\cdot3\\\\ 5kx-15y=20\\ 12x-15y=21$

Now we have  b₁=b₂ and c₁≠c₂ so the system has no solution if a₁=a₂

5k = 12

÷5     ÷5

k = ¹²/₅