Question

find the equation if the line through the intersection of lines x+2y-3=0 and 4x-y+7=0 and which is parallel to 5x+4y-20=0

Answer 1

the intersection of lines x+2y-3=0 and 4x-y+7=0
Solve x+2y-3=0 and 4x-y+7=0 Equations
x+2y-3=0 ------->eq1
4x- y+7=0 -------->eq2
eq2 × 2 => 8x - 2y +14 =0 ------->eq3

From eq2 & eq3

x + 2y - 3=0 ------->eq1
8x - 2y +14 =0 ------->eq3
---------------------
9x +11=0
X = -11/9
Therefore
x + 2y - 3=0
(-11/9) +2y = 3
(-11 + 18y)/9 =3
(-11 + 18y) =3×9
(-11 + 18y)=27
18y =27+11
18y =38
y=38/18
y =19/9
Therefore the point is (-11/9, 19/9)
Parallel to 5x+4y-20=0. (m1 = m2)
Slope m1 is from Equations above
m1 = -5/4= m2

The Equations is
y - y1 = m (x - x1)
y - 19/9 = -5/4(x +11/9)
y- 19/9 = -5x/4 - 55/36
y = -5x/4 - 55/36 + 19/9
y= (-45x -55 + 76)/36
y= (-45x + 22)/36
36y + 45x = 22 is the Equations

Answer 2

Answer:

as the two lines are parallel both the lines should have equal slope.

5x+4y-20=0__________1

x+2y-3=0____________2

4x-y+7=0____________3

from 1 we can write as slope, m =-5/4

we can write as eq. 3+eq.2multiplied by a constant k=0

and we will get

x(1+4k)+y(2-k)-3+7k______4

and we will get the slope as

-(1+4k)/(2-k)=-5/4

by solving it we will get that k=6/21

by substituting in eq 4

we will get the equation as

45x+15y-21=0

dividing by 3 we will get the final ans as

15x-5y-7

hope this helps

Step-by-step explanation: