Question

Which statement correctly explains how Kasi could find a solution to the following system of linear equations using elimination? 1-4g-15h=-17 -g+5h=13

Answer 1

{ 1-4g-15h=-17
{ -g+5h=13

{ -4g - 15h = -17 + 1
{ -g + 5h = 13

{ -4g - 15h = -16
{ -g + 5h = 13 |•3

{ -4g - 15h = -16
{ -3g +15h = 39

-4g - 15h - 3g + 15h = -16 + 39
-7g = 23
g = 23 : (-7)
g = -23/7 = -3 2/7

{ -4g - 15h = -16
{ -g + 5h = 13 | • (-4)

{ -4g - 15h = -16
{ 4g - 20h = -52

-4g - 15h + 4g - 20h = -16 - 52
-35h = -68
h = -68 : (-35)
h = 1 33/35



Control
-(-3 2/7) + 5 • 1 33/35 =
= 23/7 + 68/7 =
= 91/7 = 13

Answer 2

To solve the system of linear equations using elimination, you aim to eliminate one variable by adding or subtracting the equations in such a way that one of the variables cancels out. Here's a step-by-step process:

The system of equations is:

1. $1 - 4g - 15h = -17$
2. $-g + 5h = 13$

Let's eliminate $g$ by multiplying the second equation by 4 and then adding the two equations:

1. $1 - 4g - 15h = -17$
2. $-4g + 20h = 52$ (Multiply the second equation by 4)

Now add the two equations:

$1 - 4g - 15h + (-4g + 20h) = -17 + 52$

Combine like terms:

$-8g + 5h = 35$

Now, you have a new equation with only $g$ and $h$, and you can solve this equation simultaneously with one of the original equations to find the values of $g$ and $h$.

The new system is:

1. $-8g + 5h = 35$
2. $-g + 5h = 13$

You can now solve these equations using methods like substitution or elimination to find the values of $g$ and $h$.