hello i need help with system of equations theres 3 only thank you
2x+3y-17
3x+y=31
2(x-3y)=24
y=3x-2
2(x+4)=24
x+y=17
Hello! I can help you with solving these systems of equations. To find the solution, we'll use different methods depending on the type of system.
1. Let's solve the first system of equations:
Equations:
2x + 3y = 17 ...(1)
3x + y = 31 ...(2)
To solve this system, we can use the substitution method or the elimination method. Let's use the elimination method:
Multiply equation (2) by 2 to eliminate y:
2 * (3x + y) = 2 * 31
6x + 2y = 62 ...(3)
Now, we'll subtract equation (1) from equation (3):
(6x + 2y) - (2x + 3y) = 62 - 17
6x - 2x + 2y - 3y = 45
4x - y = 45 ...(4)
Next, we'll solve equation (4) for y:
-y = 45 - 4x
y = 4x - 45 ...(5)
Substitute equation (5) into equation (1):
2x + 3(4x - 45) = 17
2x + 12x - 135 = 17
14x - 135 = 17
14x = 17 + 135
14x = 152
x = 152 / 14
x = 10.857
Now, substitute the value of x into equation (5) to find y:
y = 4(10.857) - 45
y = 43.428 - 45
y = -1.572
Therefore, the solution to the first system of equations is x ≈ 10.857 and y ≈ -1.572.
2. Let's solve the second system of equations:
Equations:
2(x - 3y) = 24 ...(1)
y = 3x - 2 ...(2)
We can solve this system by substitution. Let's substitute equation (2) into equation (1):
2(x - 3(3x - 2)) = 24
2(x - 9x + 6) = 24
2(-8x + 6) = 24
-16x + 12 = 24
-16x = 24 - 12
-16x = 12
x = 12 / -16
x = -0.75
Now, substitute the value of x into equation (2) to find y:
y = 3(-0.75) - 2
y = -2.25 - 2
y = -4.25
Therefore, the solution to the second system of equations is x = -0.75 and y = -4.25.
3. Let's solve the third system of equations:
Equations:
2(x + 4) = 24 ...(1)
x + y = 17 ...(2)
To solve this system, we'll first solve equation (1) for x:
2(x + 4) = 24
2x + 8 = 24
2x = 24 - 8
2x = 16
x = 16 / 2
x = 8
Now, substitute the value of x into equation (2):
8 + y = 17
y = 17 - 8
y = 9
Therefore, the solution to the third system of equations is x = 8 and y = 9.
I hope this helps! Let me know if you have any other questions.