Q12 find the value(s) of k.12.For the two non-parallel straight lines L:2x- 5y+ 21 = 0 and L: 3x + y+ 6 = 0, find the coordinates oftheir intersection.Explain13.Do the two straight lines L.:10x – 8y – 3 = 0 and L,: -15x + 12y + 8 = 0 intersect? Explain your answer.

Consider the following: Line-1: 2x−5y+21=0Line-2: 3x+y+6=0 At intersection point: L1=L2…

Answered: 12. For the two non-parallel straight…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Q12

find the value(s) of k.
12.
For the two non-parallel straight lines L:2x- 5y+ 21 = 0 and L: 3x + y+ 6 = 0, find the coordinates of
their intersection.
Explain
13.
Do the two straight lines L.:10x – 8y – 3 = 0 and L,: -15x + 12y + 8 = 0 intersect? Explain your answer.

Expert Solution

Step 1

Consider the following:

$\begin{array}{l} Line-1: 2 x - 5 y + 21 = 0 \\ Line-2: 3 x + y + 6 = 0 \end{array}$

At intersection point: $L_{1} = L_{2}$

$\begin{array}{l} 2 x - 5 y + 21 = 0 \dots \dots (1) \\ 3 x + y + 6 = 0 \dots \dots (2) \\ Mutiply Equation (1) by 3 and Equation (2) by 2, \\ (2 x - 5 y + 21) \times 3 = 0 \times 3 \\ 6 x - 15 y + 63 = 0 \dots \dots (L_{1}) \\ (3 x + y + 6) \times 2 = 0 \times 2 \\ 6 x + 2 y + 12 = 0 \dots \dots (L_{2}) \\ 6 x - 15 y + 63 = 6 x + 2 y + 12 \\ 15 y + 2 y = 63 - 12 \\ 17 y = 51 \\ y = 3 \end{array}$

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