Question

How many solutions does the system below have?
y = x+1
2y - x = 2

Answer 1

1

Explanation:

There is only 2 equations, and 2 unknowns shown on this question. Which means that there could only be one point of intersection.

Answer 2

Only one solution

`y = x + 1 \\ \implies \: x - y + 1 = 0..(1) \\\implies \: a_1x + b_1y+ c_1 = 0 \\ a_1 = 1, \: \:b_1 = - 1, \: \: c_1 = 1\\ 2y - x = 2 \\ \implies x - 2y + 2 = 0 \\ \implies \: a_2x + b_2y + c_2 = 0 \\ a_2 = 1, \: \:b_2 = - 2, \: \: c_2 = 2 \\ \\ (a_1)/(a_2) = (1)/(1) = 1 \\ \\ (b_1)/(b_2) = ( - 1)/( - 2) = ( 1)/( 2) \\ \\ \because \: (a_1)/(a_2) \\eq (b_1)/(b_2) \\ \therefore \: given \: system \: of \: linear \: equations \: \\ has \: \bold\red{\boxed{only \: one}} \: solution.`