Question
Consider the system of equations shown below to answer questions 26 and 27.
{6x-3y=18
{-3x-9y=-93
In order to solve this system of equations using the elimination/combination method, the first thing Emma should do is
Answer choices:
multiply the first equation by 3
multiply the first equation by -2
multiply the second equation by 2
multiply the second equation by -3
answer CORRECTLY
{6x-3y=18
{-3x-9y=-93
In order to solve this system of equations using the elimination/combination method, the first thing Emma should do is
Answer choices:
multiply the first equation by 3
multiply the first equation by -2
multiply the second equation by 2
multiply the second equation by -3
answer CORRECTLY
Answers
GPT 3.5
The first thing Emma should do is multiply the first equation by -2.
The value of the x will be
-3
7
8
18
answer CORRECTLY
-3
7
8
18
answer CORRECTLY
GPT 3.5
To solve the system of equations using the elimination/combination method, let's multiply the first equation by -2:
(-2)(6x - 3y) = (-2)(18)
-12x + 6y = -36
The system of equations becomes:
-12x + 6y = -36
-3x - 9y = -93
We can now add the two equations together:
(-12x + 6y) + (-3x - 9y) = (-36) + (-93)
-12x - 3x + 6y - 9y = -36 - 93
-15x - 3y = -129
Now, let's solve this equation for x:
-15x - 3y = -129
-15x = -129 + 3y
x = (-129 + 3y) / -15
x = (-3(43 - y)) / -15
x = (43 - y) / 5
Since we don't have an exact value for y, we cannot determine the exact value of x. Therefore, the correct answer is not listed among the given options.
(-2)(6x - 3y) = (-2)(18)
-12x + 6y = -36
The system of equations becomes:
-12x + 6y = -36
-3x - 9y = -93
We can now add the two equations together:
(-12x + 6y) + (-3x - 9y) = (-36) + (-93)
-12x - 3x + 6y - 9y = -36 - 93
-15x - 3y = -129
Now, let's solve this equation for x:
-15x - 3y = -129
-15x = -129 + 3y
x = (-129 + 3y) / -15
x = (-3(43 - y)) / -15
x = (43 - y) / 5
Since we don't have an exact value for y, we cannot determine the exact value of x. Therefore, the correct answer is not listed among the given options.