Answer:
-6, 2
Explanation:
To solve the system of equations 3x+5y+8=0 and 4x+13y-2=0 using the elimination method, we need to eliminate one variable by adding or subtracting the equations.
Let's start by multiplying the first equation by 4 and the second equation by 3 to make the coefficients of x in both equations the same:
4(3x+5y+8) = 4(0)
3(4x+13y-2) = 3(0)
This simplifies to:
12x + 20y + 32 = 0
12x + 39y - 6 = 0
Now, we can subtract the two equations to eliminate the x variable:
(12x + 20y + 32) - (12x + 39y - 6) = 0 - 0
This simplifies to:
12x - 12x + 20y - 39y + 32 + 6 = 0
Which further simplifies to:
-19y + 38 = 0
Now, we can solve for y by isolating the variable:
-19y = -38
y = -38 / -19
y = 2
Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:
3x + 5(2) + 8 = 0
3x + 10 + 8 = 0
3x + 18 = 0
3x = -18
x = -18 / 3
x = -6
Therefore, the solution to the system of equations 3x+5y+8=0 and 4x+13y-2=0 is x = -6 and y = 2.
Now, let's move on to some practice problems to solidify our understanding.
Practice problem 1:
Solve the system of equations using the elimination method:
2x + 3y = 10
4x - 5y = 2
Practice problem 2:
Solve the system of equations using the elimination method:
3x + 2y = 8
6x + 4y = 16
Try solving these problems on your own and let me know if you need any further assistance!