Question

how many solutions does the system of equations below have?
$5x - 8y = 7$
$10x - 16y = 14$
no solution
one solution
infinitely many solutions
submit

Explanation:

Step1: Analyze the two equations

The first equation is \(5x - 8y = 7\). The second equation is \(10x - 16y = 14\). Notice that if we multiply the first equation by 2, we get \(2\times(5x - 8y)=2\times7\), which simplifies to \(10x - 16y = 14\), which is exactly the second equation.

Step2: Determine the number of solutions

When two equations in a system are essentially the same (one is a multiple of the other), they represent the same line. So, every point on that line is a solution, meaning there are infinitely many solutions.

Answer:

infinitely many solutions