Question

solve each system of equations by the substitution method. Tell whether each system is inconsistent or consistent. If the system is consistent, tell whether it is independent or dependent


5x-4y=11
3x-y=1

Answer 1

5x-4y=11 ... (1)
3x-y=1 ....(2)

take one of the equations and solve for a variable in place of another variable:
eg. take equation (2) for example
3x -y =1
solve for x
add y to both sides
=> 3x -y +y = 1 +y
=> 3x =1+y
=> x = (1+y)/3 ..... (3)

Next substitute for the new x value into equation (1)

thus equation (1) becomes:
5x -4y = 11
=> 5 * (1+y)/3-4y = 11
=> 5 +5y -12y = 33 ( after multiplying by 3 on both sides)
=> -7y = 28
=> y = -4

Now substitute the new value of y in equation (3) above

Thus
x = (1+y)/3 ..(3)
=>x =(1-4)/3 = -1

Thus the solution is:

x = -1
y = -4

Answer 2

The system is consistent and independent