Question

How many solutions does this system have? y = 5 x minus 1. y = negative 3 x + 7. The system has solution(s).

Answer 1

Only one solution: (1,4)

Explanation:

y = 5x - 1

y = -3x + 7

5x - 1 = -3x + 7

8x = 8

x = 1

y = 5(1) - 1

y = 4

Only one solution: (1,4)

Answer 2

there is only 1 solution

Explanation:

Given

y = 5x - 1 --------(1)

y = -3x + 7-------(2)

Observation 1:

Both are linear equations (i.e straight lines)

Observation 2:

We can see that both lines have different slopes.

for (1), slope, m = 5

for (2), slope, m = -3

this means that both the straight lines will intersect each other at only 1 point.

Hence we can conclude that there is only 1 solution