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
Of course! I'll be happy to help you with your system of equations. Let's solve each system one by one.
1. System of Equations:
Equation 1: 2x + 3y = 17
Equation 2: 3x + y = 31
To solve this system, we can use the method of substitution or elimination. Let's use the method of substitution:
1. Solve Equation 2 for y:
y = 31 - 3x
2. Substitute the value of y in Equation 1 with 31 - 3x:
2x + 3(31 - 3x) = 17
Simplify this equation:
2x + 93 - 9x = 17
Combine like terms:
-7x = -76
Divide both sides by -7:
x = 76/7
3. Substitute the value of x in Equation 2:
y = 31 - 3(76/7)
Simplify this equation:
y = 217/7
Therefore, the solution to the first system of equations is x = 76/7 and y = 217/7.
2. System of Equations:
Equation 1: 2(x - 3y) = 24
Equation 2: y = 3x - 2
Let's solve this system using substitution:
1. Substitute the value of y in Equation 1 with 3x -2:
2(x - 3(3x - 2)) = 24
Simplify this equation:
2(x - 9x + 6) = 24
Simplify further:
2(-8x + 6) = 24
Distribute the 2:
-16x + 12 = 24
Move 12 to the other side:
-16x = 12
Divide both sides by -16:
x = -12/16
Simplify further:
x = -3/4
2. Substitute the value of x in Equation 2:
y = 3(-3/4) - 2
Simplify this equation:
y = -9/4 - 8/4
Simplify further:
y = -17/4
Therefore, the solution to the second system of equations is x = -3/4 and y = -17/4.
3. System of Equations:
Equation 1: 2(x + 4) = 24
Equation 2: x + y = 17
Let's solve this system using the method of elimination:
1. Simplify Equation 1 by distributing the 2:
2x + 8 = 24
Move 8 to the other side:
2x = 16
Divide both sides by 2:
x = 8
2. Substitute the value of x in Equation 2:
8 + y = 17
Move 8 to the other side:
y = 17 - 8
Simplify:
y = 9
Therefore, the solution to the third system of equations is x = 8 and y = 9.
I hope this explanation helps you solve the system of equations! Let me know if there's anything else I can assist you with.