To solve the given system of equations by the elimination method, we'll eliminate one variable by multiplying the equations by appropriate numbers so that the coefficients of one variable in both equations are equal.
Given equations:
1) 4x - 3y = 2
2) 8x + 12y = 10
To eliminate the y variable, we can multiply equation 1) by 4 and equation 2) by 3.
3) 16x - 12y = 8
4) 24x + 36y = 30
Now, we can add equations 3) and 4) to eliminate the y variable:
(16x - 12y) + (24x + 36y) = 8 + 30
40x + 24y = 38
The new equation obtained is:
5) 40x + 24y = 38
Now, let's divide the equation by 2 to simplify it:
(40x + 24y)/2 = 38/2
20x + 12y = 19
Now, we have two equations:
5) 20x + 12y = 19
2) 8x + 12y = 10
We can subtract equation 2) from equation 5) to eliminate the y variable:
(20x + 12y) - (8x + 12y) = 19 - 10
20x - 8x + 12y - 12y = 9
12x = 9
Dividing both sides of the equation by 12:
x = 9/12
x = 3/4
Substituting this value of x into equation 2):
8(3/4) + 12y = 10
6 + 12y = 10
12y = 10 - 6
12y = 4
y = 4/12
y = 1/3
Therefore, the solution to the given system of equations is the ordered pair:
(x, y) = (3/4, 1/3)
So, the correct choice is A. The solution set is (3/4, 1/3).
Solve the system by the elimination method.
4x−3y=
2
8x+12y=
10
.
.
.
Question content area right
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The solution set is enter your response here.
(Type an ordered pair. Type integers or simplified fractions.)
B.
There are infinitely many solutions.
The solution set is x,enter your response here, where x is any real number. (Type integers or simplified fractions.)
C.
The solution is the empty set.
1 answer