Question

1. Solve the system by any method:
2x-5y=-1
2x-y=1



How many solutions does the system of equations below have? Explain your answer.
y=3/5x-1
y=6/10x+3



plz help me ;-; i don't understand how to do this, sorry ;-;

Answer 1

1. 2x-y=1 => y=2x-1 ...
sub into equation 1 and solve for x ... 2x-5(2x-1)=-1 => 2x-10x+5=-1
=> 10x-2x=5+1
=> 8x=6 => x=(8/6)=(4/3)
Sub x into either equation and solve for y ...
2x-5y=-1
=> 2(4/3) - 5y = -1
=> 2.7 - 5y = -1
=> 2.7 + 1 = 5y
=> 3.7 = 5y
=> y = (3.7/5) = 0.74

Same procedure for 2nd set... Solve one equation for x or y, sub into the 2nd equation and solve for the variable.

Answer 2

Since both equations contain 2x, the easiest way would be elimination, thus subtract them:

-4y = -2
y = -2/-4 = 1/2

sub into the first:
2x - 5(1/2) = -1
2x = 5/2-1 = 3/2
x = 3/4 ---------> x = 3/4 , y = 1/2

#2
y=(3/5_x-1
y=6/10x+3 ----> y = (3/5)x + 3

since you have two lines with the same slope, but different y-intercepts, you have two distinct parallel lines.
Which of course cannot meet, so
there is no solution