Question

How many solutions does this linear system have?

y = 2x – 5

–8x – 4y = –20

one solution: (–2.5, 0)
one solution: (2.5, 0)
no solution
infinite number of solutions

Answer 1

One solution: (2.5, 0)

Work: Substitute y = 2x − 5 into −8x − 4y = −20:
−8x − 4(2x − 5) = −20 → −8x − 8x + 20 = −20 → −16x = −40 → x = 2.5, y = 2(2.5) − 5 = 0.