Question

x 5x - 2y = 3
-5x + 4y = 9
Solve the system of equations.
X
A x = 6, y = 3
B
C
D
E
1
x = 6, y = 13.
2
x = 3, y = 6
x = 1, y =0
x = -3, y = -6

Answer 1

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of elimination.

First, let's multiply the first equation by 4 and the second equation by 5 to make the x terms cancel out when we add the equations together:
4(5x - 2y) = 4(3)
5(-5x + 4y) = 5(9)
20x - 8y = 12
-25x + 20y = 45

Now let's add the two equations together:
(20x - 8y) + (-25x + 20y) = 12 + 45
-5x + 12y = 57

Now we have a new equation: -5x + 12y = 57

Let's rearrange this equation to solve for x:
-5x = -12y + 57
x = (12y - 57)/(-5)

Now let's substitute this expression for x into one of the original equations. Let's use the first equation:
x + 5x - 2y = 3
(12y - 57)/(-5) + 5(12y - 57)/(-5) - 2y = 3
(12y - 57 + 60y - 285)/(-5) - 2y = 3
(72y - 342)/(-5) - 2y = 3

Let's simplify and solve for y:
(-72y + 342)/5 - 2y = 3
(-72y + 342) - 10y = 15
-72y - 10y + 342 = 15
-82y + 342 = 15
-82y = -327
y = (-327)/(-82)
y ≈ 3.988

Now let's substitute this value of y back into the expression for x:
x = (12y - 57)/(-5)
x = (12(3.988) - 57)/(-5)
x = (-4.544)/(-5)
x ≈ 0.909

So the solution to the system of equations is approximately x = 0.909 and y = 3.988.

Therefore, the correct answer is A. x = 0.909, y = 3.988.