Math Problem : Solving Systems of Equations and Inequalities .?

Question

EXPLAIN THIS PROBLEM TO ME .

2x + y = -4
5x + 3y = -6


the point at which they meet at the graph .
without graphing it .
using substitution and elimination .
explain .
you'll get best answer .

Answer 1

you can either use substitution or elimination to solve systems of equations.

Substitution:
you solve one of the equations for x or y and substitute that value into the other equation, and solve

ex. 2x + y = -4
so y=-2x -4

now substitute this value of y into the 2nd equation
5x + 3y = -6
5x + 3(-2x -4) = -6
5x -6x -12 = -6
-x = 6
x=-6

now you can use the value of x to find y
2x + y = -4
2(-6) + y = -4
-12 + y =-4
y=8

thus the point of intersection is (-6,8), the point which satisfys both equations

Elimination: you manipulate both equations so that you can "eliminate" one of the variables

2x+y=-4
5x+3y=-6

which variable do you want to eliminate? I'll choose y
so if you multiply throught the first equation by -3,
you get
-6x -3y =12
5x + 3y =-6
now you can eliminate the y term
-x=6
x=-6

plug in x to one of the equations to find y:
2x + y = -4
2(-6) + y = -4
-12 + y = -4
y = 8

so you get the same intersection point (-6, 8) using both methods

Answer 2

solve for y and then substitute into other equation.
2x+y=-4
y=-2x-4
5x+3y=-6
5x+3(-2x-4)=-6
5x-6x-12=-6
-x=6
x=-6
y=-2x-4= -2(-6)-4 =8

coordinates are (-6,8)

Answer 3

i think it is -3x +4y=-10

put - on the 2x then add them together then you should get that answere
i should be atleast close
i did this last year