Question

Solve by substitution or elimination 5x+3y=-15 -8x-2y=10

Answer 1

Answer: The required solution is (x, y) = (0, -5).

Step-by-step explanation: We are given to solve the following system of equations by the method of substitution or elimination :

`5x+3y=-15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-8x-2y=10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

We will be solving the given system by substitution method.

From equation (ii), we have

`-8x-2y=10\\\\\Rightarrow -4x-y=5\\\\\Rightarrow y=-4x-5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)`

Substituting the value of y from equation (iii) in equation (i), we get

`5x+3(-4x-5)=-15\\\\\Rightarrow 5x-12x-15=-15\\\\\Rightarrow -7x=0\\\\\Rightarrow x=0.`

From equation (iii), we get

`y=-4*0-5=-5.`

Thus, the required solution is (x, y) = (0, -5).

Answer 2

x=0, y=-5

Explanation:

The system is

(1) 5x+3y=-15

(2) -8x-2y=10

Let's solve it by elimination. In order to do it, you have to multiply the equations by suitable numbers in such a way that when you add the 2 equations, one of the unknowns is eliminated

Multiply (1) by 2 and (2) by 3

(1) 10x+6y=-30

(2) -24x-6y=30

Add the two equations

10x-24x+6y-6y=-30+30 ----> -14x=0---->x=0

Now replace this value in any equation, for example in (1)

6y=-30 ----> y=-30/6----> y=-5