Respuesta :
ANSWER
y = 2x - 7
EXPLANATION
We have that the line is parallel to y = 2x + 1 and it passes through the solution of:
3x - 2y = 10
x + y = 5
Parallel lines have the same slope.
So, the slope of the line we are looking for will be the same as the slope of y = 2x + 1.
Linear equations are given generally as:
y = mx + c
where m = slope, c = y intercept
This means that the slope of the line is 2.
Now, we need to find the solution of the smultaneous equations given to know the point it passes through.
We have:
3x - 2y = 10
x + y = 5
From the second equation:
x = 5 - y
Put that in the first:
3(5 - y) - 2y = 10
15 - 3y - 2y = 10
Collect like terms:
-5y = 10 - 15 = -5
=> y = -5 / -5
y = 1
Therefore:
x = 5 - y = 5 - 1
x = 4
Therefore, the line passes through (4, 1)
We can now use the point-slope method to find the equation of the line:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where m = 2 and (x1, y1) = (4, 1)} \\ \Rightarrow\text{ y - 1 = 2(x - 4) = 2x - 8} \\ \text{Collect like terms:} \\ y\text{ = 2x - 8 + 1} \\ y\text{ = 2x - 7} \end{gathered}[/tex]That is the equation of the line.
