How do solve the following linear system?: 11x + 3y + 7 = 0 , -6x-2y=-8 ?

2 Answers
Jun 20, 2018

x=-19/2,y=65/2

Explanation:

Multiplying the first equation by 2 and the second equation by 3 and adding both

4x=-38
so
x=-19/2
plugging this in the second equation
-6(-19/2)-2y=-8
57-2y=-8
-2y=-65

y=65/2

Jun 20, 2018

x=-19/2 and y=65/2

Explanation:

Given
[1]color(white)("XXX")11x+3y+7=0
[2]color(white)("XXX")-6x-2y=-8

To make this easier to work with I will convert [1] into the same standard form as [2] by subtracting 7 from both sides
[3]color(white)("XXX")11x+3y=-7

We need to eliminate one of the variables (either x or y) by combining these two equations.
For example, we might decide to eliminate the term containing the variable y.

To do this we need to convert equations [2] and [3] into equivalent forms with identical magnitude coefficients for y.

The least common multiple for the (magnitude of)coefficients of y in [2] and [3] is 6, so we will convert each of [2] and [3] into equivalent forms with a term +-6y.

Multiplying [2] by 3
[4]color(white)("XXX")-18x-6y=-24
Multiplying [3] by 2
[5]color(white)("XXX")22x+6y=-14

Now if we add [4] and [5], we can eliminate the y term:
[6]color(white)("XXX")4x=-38

Dividing both sides of [6] by 4 we get
[7]color(white)("XXX")x=-19/2

We can now substitute (-19/2) for x back in one of our original equations. For demonstration purposes I will use equation [2]
[8]color(white)("XXX")-6 * (-19/2)-2y=-8

Simplifying
[9]color(white)("XXX")57-2y=-8

[10]color(white)("XXX")-2y=-65

[11]color(white)("XXX")y=65/2

Giving the final solution
color(white)("XXX")x=-19/2 " or " -9 1/2
and
color(white)("XXX")y=65/2" or " 32 1/2

[Since we used [2] to develop the value for y we should check this answer using [1] to verify that our results are correct].