What is the intersection point in the graph of the lines
5x-11=4y and 7x-1=8y
2006-10-04 12:31:20 · 3 answers · asked by someguy 2 in Education & Reference ➔ Homework Help
5x/4-11/4 = 7x/8-1/8
10x/8-22/8 = 7x/8-1/8
10x/8-7x/8-22/8-1/8 = 3x/8-21/8 = 24x-168
x=-168/-24= 7
if x=7 then y = 49/8-1/8 = 48/8 = 6
the intersection point is
(7,6)
2006-10-04 12:50:29 · answer #1 · answered by meetha 4 · 0⤊ 0⤋
simultaneous equations "elimination method"
(1)5x-11 =4y
(2)7x-1 =8y [double (1) equation to get same values for y]
(1)10x-22=8y [subtract (2) from (1)]
3x-21 =0
3x=21
x=7 [substitute back into (1) equation]
5(7)-11=4y
35-11=4y
24=4y
y=6 [check with (2) equation]
LHS=7(7) -1
=49-1
=48
RHS=8(6)
=48
therefore LHS=RHS [which means its correct]
point of intersection, x=7, y=6 so.... pnt of int = (7,6)
2006-10-04 19:44:13 · answer #2 · answered by ed-dg 2 · 0⤊ 0⤋
get the 2 equations into y-int form (y=mx+b)
5x-11=4y
y=5/4(x)-11/4
7x-1=8y
y=7/8(x)-1/8
because they intersect, the 2 lines will have the same (x,y) value at one point. So using that logic, you can let both their y values equal to each other and solve for x:
y=5/4(x)-11/4
y=7/8(x)-1/8
5/4(x)-11/4 = 7/8(x)-1/8
5/4(x) - 7/8(x) = 11/4 - 1/8
10/8(x) - 7/8(x) = 22/8 - 1/8
3/8(x) = 21/8
3x=21
x=7
now plug x=7 into any of the 2 original equations and get the y value.
2006-10-04 19:40:22 · answer #3 · answered by Mr.Moo 4 · 0⤊ 0⤋