Solve the following system of equations using the elimination method. 3x−4y=−4 , x+3y=−10 (1 point) Responses (−2,−4) left parenthesis negative 2 comma negative 4 right parenthesis (−16,2) left parenthesis negative 16 comma 2 right parenthesis (−16,−2) left parenthesis negative 16 comma negative 2 right parenthesis (−4,−2)
To solve the system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the two equations.
By multiplying the second equation by 4, we can eliminate the y variable:
3x − 4y = −4
4(x + 3y) = 4(-10)
Expanding the equation:
3x - 4y = -4
4x + 12y = -40
Now we can subtract the first equation from the second equation:
(4x + 12y) - (3x - 4y) = -40 - (-4)
Simplifying:
4x + 12y - 3x + 4y = -40 + 4
x + 16y = -36
So the simplified system of equations is:
x + 16y = -36
3x - 4y = -4
To solve for x, we can multiply the first equation by 3 and the second equation by 1 to make the coefficients of x the same:
3(x + 16y) = 3(-36)
3x + 48y = -108
3x - 4y = -4
Now we can subtract the second equation from the first equation:
(3x + 48y) - (3x - 4y) = -108 - (-4)
Simplifying:
3x + 48y - 3x + 4y = -108 + 4
52y = -104
Solving for y by dividing both sides by 52:
y = -104/52
y = -2
Now we can substitute the value of y into one of the original equations to solve for x. Let's use the first equation:
3x - 4(-2) = -4
3x + 8 = -4
3x = -12
x = -12/3
x = -4
So the solution to the system of equations is (-4, -2), or in coordinate form: (-4,-2).