Solve the system of equations by elimination.%0D%0A%0D%0A3x + 4y = 31%0D%0A2x – 4y = –6%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A(4, 5)%0D%0A(4, 5)%0D%0A%0D%0A(5, 4)%0D%0A(5, 4)%0D%0A%0D%0A(–5, 12.5)%0D%0A(–5, 12.5)%0D%0A%0D%0A(5, –4)
To solve the system of equations by elimination, we can add the two equations together to eliminate the variable "y".
(3x + 4y) + (2x - 4y) = 31 + (-6)
Combining like terms:
5x = 25
Dividing both sides of the equation by 5:
x = 5
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y.
Using the first equation:
3(5) + 4y = 31
15 + 4y = 31
Subtracting 15 from both sides of the equation:
4y = 16
Dividing both sides of the equation by 4:
y = 4
Therefore, the solution to the system of equations is x = 5 and y = 4. So, the correct response is (5, 4).
To solve the system of equations by elimination, we'll add the two equations together to eliminate the variable "y":
(3x + 4y) + (2x - 4y) = 31 + (-6)
Combining like terms:
5x = 25
Divide both sides by 5 to solve for x:
x = 5
Now substitute the value of x back into either of the original equations, let's use the first equation:
3(5) + 4y = 31
15 + 4y = 31
Subtract 15 from both sides:
4y = 16
Divide both sides by 4 to solve for y:
y = 4
So the solution to the system of equations is (x, y) = (5, 4).
Therefore, the correct response is:
(5, 4)
To solve the system of equations by elimination method, follow these steps:
Step 1: Write down the given system of equations:
3x + 4y = 31 ...(Equation 1)
2x - 4y = -6 ...(Equation 2)
Step 2: Add the two equations to eliminate the 'y' variable. When we add the equations, the resulting equation will eliminate the 'y' term since 4y and -4y will cancel each other out:
(3x + 4y) + (2x - 4y) = 31 + (-6)
Simplifying the equation:
3x + 2x + 4y - 4y = 25
5x + 0 = 25
5x = 25
Divide both sides of the equation by 5:
5x/5 = 25/5
x = 5
Step 3: Substitute the value of x (= 5) back into one of the original equations to find the value of y. Let's use Equation 1:
3x + 4y = 31
3(5) + 4y = 31
15 + 4y = 31
Subtract 15 from both sides:
4y = 31 - 15
4y = 16
Divide both sides by 4:
4y/4 = 16/4
y = 4
Step 4: Write the solution as an ordered pair (x, y):
The solution to the system of equations is (x, y) = (5, 4).
Therefore, the correct answer is (5, 4).