Question

Please please help me!!

solve the system of equations by using the substitution method.
{ 4x - 5y = 19
{ y = x - 4

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution is __. (simplify your answer. Type an ordered pair.)
B. There are infinitely many solutions.
C. There is no solution.

Answer 1

`\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}`

`x=1,\:y=-3`

As the system of equations has only one solution, thus the solution consistent.

Explanation:

Given the system of equations

4x - 5y = 19

y = x - 4

Solving the system of equations by using the substitution method.

`\begin{bmatrix}4x-5y=19\\ y=x-4\end{bmatrix}`

`\mathrm{Subsititute\:}y=x-4`

`\begin{bmatrix}4x-5\left(x-4\right)=19\end{bmatrix}`

`4x-5\left(x-4\right)=19`

`-x+20=19`

isolate x for
`-x+20=19`

`-x+20=19`

`-x=-1`

Divide both sides by -1

`(-x)/(-1)=(-1)/(-1)`

`x=1`

`\mathrm{For\:}y=x-4`

`\mathrm{Subsititute\:}x=1`

`y=1-4`

`y=-3`

`\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}`

`x=1,\:y=-3`

As the system of equations has only one solution, thus the solution consistent.

Please remember that if the system of equations has only one solution, then it is an independent system of equations.