In the first system, x = 10 and y = 4. In the second system, x = 4 and
y = 5. In the third system, x = 8 and y = 2.
4. Let's solve the system of equations:
1. Equation 1: 5x + 2y = 58
2. Equation 2: y = 14 - x
Substitute the expression for y from Equation 2 into Equation 1:
5x + 2(14 - x) = 58
Now, distribute the 2:
5x + 28 - 2x = 58
Combine like terms:
3x + 28 = 58
Subtract 28 from both sides:
3x = 30
Divide by 3:
x = 10
Now that we have the value for x, substitute it back into Equation 2 to find y:
y = 14 - x
y = 14 - 10
y = 4
So, the solution to the system is x = 10 and y = 4 .
5. Let's solve the system of equations:
1. Equation 1: 10x + 3y = 55
2. Equation 2: y = 2x - 3
Substitute the expression for y from Equation 2 into Equation 1:
10x + 3(2x - 3) = 55
Now, distribute the 3:
10x + 6x - 9 = 55
Combine like terms:
16x - 9 = 55
Add 9 to both sides:
16x = 64
Divide by 16:
x = 4
Now that we have the value for x, substitute it back into Equation 2 to find y:
y = 2x - 3
y = 2(4) - 3
y = 5
So, the solution to the system is x = 4 and y = 5.
6. Let's solve the system of equations:
1. Equation 1: 4x - 7y = 18
2. Equation 2: x = 2y + 4
Substitute the expression for x from Equation 2 into Equation 1:
4(2y + 4) - 7y = 18
Distribute the 4:
8y + 16 - 7y = 18
Combine like terms:
y + 16 = 18
Subtract 16 from both sides:
y = 2
Now that we have the value for y, substitute it back into Equation 2 to find x:
x = 2y + 4
x = 2(2) + 4
x = 8
So, the solution to the system is x = 8 and y = 2.