Question

Use the substitution method or linear combinations to solve the linear system and tell how many solutions the system has. $$ \begin{aligned}&-7 x+7 y=7\\\&2 x-2 y=-18\end{aligned} $$

Short answer

The given system of equations has no solutions because the equations represent two distinct parallel lines that don't intersect.

Step-by-step solution

- Simplify the equation

Simplify both the equations by dividing them with their respective common numbers. In the first equation, divide the entire equation by 7 and the second one by 2. So the equations after simplification will be: - \(x - y = 1\)- \(x - y = -9\)

- Compare the simplified equations

Take a look at both the simplified equations. They have the same left side but different right side, this means they are parallel lines. But two distinct parallel lines do not intersect.

- Determine the number of solutions

As the two lines do not intersect, there will be no solution to the system of equations. Hence, the number of solutions for this system is zero.