can you solve this set of equations using the elimination method?
3x+4y=34 and 3x+2y=26
3x+4y=34
3x+2y=26
(1)3X+4Y=34
(-1)3X+2Y=26
3X+4Y=34
-3X+(-2Y)=-26
6Y=60
Y=10
3X+2(10)=26
3X+20=26
3X=26-20
3X=6
X=2
???
4y-2y=34-26
Yes, I can solve the set of equations using the elimination method. The elimination method involves adding or subtracting the equations in a way that cancels out one of the variables, allowing us to solve for the remaining variable.
Let's start by multiplying the second equation by 2, so that the coefficients of y in both equations become the same:
First equation: 3x + 4y = 34
Second equation (multiplied by 2): 6x + 4y = 52
Now, we can subtract the first equation from the second equation:
(6x + 4y) - (3x + 4y) = 52 - 34
Simplifying:
6x - 3x + 4y - 4y = 18
This simplifies to:
3x = 18
Now we can solve for x:
x = 18 / 3
x = 6
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:
3(6) + 4y = 34
Simplifying:
18 + 4y = 34
Subtracting 18 from both sides:
4y = 34 - 18
4y = 16
Dividing both sides by 4:
y = 16 / 4
y = 4
Therefore, the solution to the set of equations is x = 6 and y = 4.