x + 3y = 5
-x + 6y = 4
Solve the system of equations.
Responses
A x = 6, y = 1x = 6, y = 1
B x = 0, y = 2x = 0, y = 2
C x = 2, y = 1x = 2, y = 1
D x = 1, y = 1x = 1, y = 1
E x = 1, y = 2x = 1, y = 2
D x = 1, y = 1 (Solution: x = 1, y = 1 can be obtained by adding the two equations to eliminate x, resulting in 9y = 9, and then solving for y. Substituting y = 1 into either of the original equations gives x = 1.)
To solve the system of equations:
1. Start by multiplying the first equation by -1 to eliminate the x term.
-x + 3y = -5
2. Now, add this new equation to the second equation to cancel out the x term.
-x + 6y = 4
+ (-x + 3y = -5)
--------------------------------
9y = -1
3. Divide both sides of the equation by 9 to solve for y.
9y / 9 = -1 / 9
y = -1/9
4. Substitute the value of y back into one of the original equations to solve for x.
x + 3(-1/9) = 5
x - 1/3 = 5
5. Add 1/3 to both sides of the equation to isolate x.
x - 1/3 + 1/3 = 5 + 1/3
x = 5 + 1/3
Therefore, the solution to the system of equations is:
x = 5 + 1/3 and y = -1/9.
Simplifying the value of x:
x = 5 + 1/3
x = 15/3 + 1/3
x = 16/3
So, the correct answer is:
B) x = 16/3, y = -1/9