Question

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.

4x - y = 2
25x-6y=12

Answer 1

From the first equation, we can solve for y in terms of x:

4x - y = 2

y = 4x - 2

Now, we can substitute this expression for y into the second equation:

25x - 6y = 12

25x - 6(4x - 2) = 12

25x - 24x + 12 = 12

x = 0

Substituting this value of x into the first equation, we get:

4x - y = 2

4(0) - y = 2

y = -2

So, the solution to the system is (x,y) = (0,-2).

Therefore, the system has a unique solution and is consistent.