How do I solve the system 3x-2y=-4 and -5x+y=3?

Question

How do I solve the system 3x-2y=-4 and -5x+y=3? Please give the steps; not just the answer! If you want to help me even more you can tell me how to write the equation of the line that passes through the points (-3,2) and (-4,6). Thanks!

Answer 1

3x-2y=-4 (1)

-5x+y=3 (2)

Let's use a substitution method.

(2) gives : y=3+5x

Let's put it in (1).

3x-2(3+5x)=-4

3x-6-10x=-4

-7x=2

x=-2/7

y can then be calculated.

y=3+5(-2/7)=11/7

The solution of the system of equations is

x=-2/7

y=11/7

Let's solve the other problem.

Let's note A the point of coordinates (-3,2).

Let's note B the point of coordinates (-4,6)

A directing vector of the line (AB) has got the components

(-1,4)

A point M(x,y) of the line AB is so that the vectors AB and AM are colinear.

det(AB,AM)=0

-1(y-2)-4(x-(-3))=0

4x+y+10=0