Question

Solve the following system of linear equations by substitution and determine whether the system has one solution, no solution, or aninfinite number of solutions. If the system has one solution, find the solution.-5x + y = -125y = 10x - 15

Answer 1

Dividing the second equation by 5 we get:

$\begin{gathered} \frac{5y}{5}=\frac{10x-15}{5}, \\ y=2x-3. \end{gathered}$

Substituting the last equation in the first one we get:

$-5x+2x-3=-12.$

Adding like terms we get:

$-3x-3=-12.$

Adding 3 to the above equation we get:

$\begin{gathered} -3x-3+3=-12+3, \\ -3x=-9. \end{gathered}$

Dividing the above equation by -3 we get:

$\begin{gathered} \frac{-3x}{-3}=\frac{-9}{-3}, \\ x=3. \end{gathered}$

Finally, substituting x=3 in y=2x-3 we get:

$\begin{gathered} y=2\cdot3-3, \\ y=6-3. \\ y=3. \end{gathered}$

Answer: One solution (3,3).