Write the equation of the line that is parallel to y=2x+1 and passes throughthe solution of these equations 6x-2y=20 and x+y=5
We want the equation of a line and that is y = mx + c.
We need to find m and c.
We are told that our line is parallel to the line y = 2x + 1
That means that they have the same gradient.
The gradient of y = 2x + 1 is 2. Therefore m = 2
We are told that our line passes through the solution of the equations 6x-2y=20 and x+y=5.
Solving trhe equations
6x - 2y = 20
x + y = 5
Dividing the 1st equation by 2,
3x - y = 10
x + y = 5
Now add the 2 equations, to get
4x = 15
Giving, x = 3 3/4, y = 1 1/4
Since (x, y) = (15/4, 5/4) is also a solution to our line, y = 2x + c (using m = 2), then we can substitute in these values for x and y and hence solve for c.
5/4 = 2(15/4) + c
5 = 30 + 4c
4c = -25
c = -25/4
Our equation then is: y = 2x - 25/4