Question

-11y = 6(2+1) - 13y

4y - 24 = c(z – 1)
For what value of c does the above system of linear equations in the variables y and z have
infinitely many solutions?

Answer 1

12

Explanation:

Let's put the equations in standard form. For the first equation, we have:

−11y=6(z+1)-13y

2y−6z=6

y−3z=3

The second equation is:

4y−24=c(z−1)

4y−cz=24−c

If we multiply the first equation by 4, we get:

4y-12z=12

Comparing the two equations, we see that if c=12, both equations will be the same and there will be infinitely many solutions.

The correct value of c is 12.