i only need help on these two that's it so please help me(step by step if you could)
1)1.5x-2.5y=8.5 6x+30y=24
2)3x-2y=8 x+3/2y=8
THANKS SO MUCHHHHH!! :))))
1) To solve the system of equations:
Step 1: Choose one of the equations and solve for one variable in terms of the other variable. Let's solve the first equation for x in terms of y:
1.5x - 2.5y = 8.5
Add 2.5y to both sides of the equation:
1.5x = 2.5y + 8.5
Divide both sides by 1.5:
x = (2.5y + 8.5) / 1.5
Step 2: Substitute the value of x obtained from Step 1 into the second equation:
6x + 30y = 24
Replace x with (2.5y + 8.5) / 1.5:
6((2.5y + 8.5) / 1.5) + 30y = 24
Simplify the expression:
(15y + 51) + 30y = 24
Combine like terms:
45y + 51 = 24
Subtract 51 from both sides:
45y = -27
Divide by 45:
y = -27 / 45 = -0.6
Step 3: Substitute the value of y back into the equation obtained in Step 1 to solve for x:
x = (2.5(-0.6) + 8.5) / 1.5
Simplify the expression:
x = (2.5y - 1.5 + 8.5) / 1.5
x = (2.5(-0.6) + 7) / 1.5
x = (-1.5 + 7) / 1.5
x = 5.5 / 1.5
x = 3.67
Therefore, the solution to the system of equations is x = 3.67 and y = -0.6.
2) To solve the system of equations:
Step 1: Choose one of the equations and solve for one variable in terms of the other variable. Let's solve the second equation for x in terms of y:
x + (3/2)y = 8
Subtract (3/2)y from both sides of the equation:
x = 8 - (3/2)y
Step 2: Substitute the value of x obtained from Step 1 into the first equation:
3x - 2y = 8
Replace x with 8 - (3/2)y:
3(8 - (3/2)y) - 2y = 8
Expand the expression:
24 - (9/2)y - 2y = 8
Combine like terms:
24 - (13/2)y = 8
Subtract 24 from both sides:
-(13/2)y = -16
Multiply both sides by -2/13:
y = (-16)(-2/13)
y = 32/13
Step 3: Substitute the value of y back into the equation obtained in Step 1 to solve for x:
x = 8 - (3/2)(32/13)
x = 8 - (96/26)
x = 8 - (48/13)
x = (104/13) - (48/13)
x = 56/13
Therefore, the solution to the system of equations is x = 56/13 and y = 32/13.