Question

Solve the following system of equations using the elimination method.3x−4y=−4 , x+3y=−10(1 point)Responses(−4,−2)left parenthesis negative 4 comma negative 2 right parenthesis(−16,−2)left parenthesis negative 16 comma negative 2 right parenthesis(−2,−4)left parenthesis negative 2 comma negative 4 right parenthesis(−16,2)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the equations.

In this case, let's eliminate the variable x. To do so, we'll multiply the second equation by 3 and the first equation by -1 (to make the coefficients of x the same but opposite):

-1*(3x - 4y) = -1*(-4)
3*(-x - 3y) = 3*(-10)

Simplifying these equations, we get:

-3x + 4y = 4
-3x - 9y = -30

Now, we'll add the two equations together to eliminate x:

(-3x + 4y) + (-3x - 9y) = 4 + (-30)
-6x - 5y = -26

To solve for y, we can multiply the entire equation by -1 to make the coefficient of y positive:

-1*(-6x - 5y) = -1*(-26)
6x + 5y = 26

Now, we have a new system of equations:

-3x - 9y = -30
6x + 5y = 26

To eliminate y, we can multiply the first equation by 5 and the second equation by 9 to make the coefficients of y the same but opposite:

5*(-3x - 9y) = 5*(-30)
9*(6x + 5y) = 9*(26)

Simplifying these equations, we get:

-15x - 45y = -150
54x + 45y = 234

Now, we'll add the two equations together to eliminate y:

(-15x - 45y) + (54x + 45y) = -150 + 234
39x = 84

Dividing both sides of the equation by 39, we get:

x = 84/39
x = 28/13

Now, substitute this value of x back into one of the original equations to solve for y. Let's use the first equation:

3*(28/13) - 4y = -4
84/13 - 4y = -4

Multiplying both sides of the equation by 13 to get rid of the fraction:

84 - 52y = -52

Now, subtract 84 from both sides of the equation:

-52y = -52 - 84
-52y = -136

Finally, divide both sides of the equation by -52 to solve for y:

y = -136/-52
y = 34/13

So, the solution to the system of equations is:

x = 28/13 and y = 34/13

Therefore, the correct option is: (28/13, 34/13)