Question

For what value(s) of h is the linear system consistent?
{4x₁-20x₂ = h ;
-2x₁+10x₂ =9

Answer 1

The values of h for which the linear system is consistent are any value of h, as indicated by the equation 0 = h+18.

Step-by-step explanation:

In order to determine the values of h for which the linear system is consistent, we can solve the system of equations using the method of elimination. Firstly, we can multiply the second equation by 2 to make the coefficients of x₁ match:

4x₁ - 20x₂ = h

-4x₁ + 20x₂ = 18

Adding the two equations together, we can eliminate x₁:

0 = h + 18

From this equation, we can see that the system is consistent for any value of h as 0 is equal to h+18.