Final answer:
To solve the first system of equations, use the substitution method to find x = 15 and y = 5. To solve the second system of equations, use the elimination method to find x = 17.05 and y = 7.75.
Step-by-step explanation:
To solve the system of equations:
a) 2x-4y=10 and x+5y=40
We can solve this system using the method of substitution. We solve one equation for one variable and substitute it into the other equation.
From the second equation, we can solve for x in terms of y:
x = 40 - 5y
Substitute x into the first equation:
2(40 - 5y) - 4y = 10
80 - 10y - 4y = 10
80 - 14y = 10
-14y = -70
y = 5
Substitute y back into x = 40 - 5y:
x = 40 - 5(5)
x = 15
Therefore, the solution to the system of equations is x = 15 and y = 5.
b) 3x-5y=4 and -2x+6y=18
We can solve this system of equations using the method of elimination. We multiply the first equation by 2 and the second equation by 3 to make the coefficients of x in both equations equal but opposite in sign.
2(3x - 5y) = 2(4)
-2(-2x + 6y) = -2(18)
6x - 10y = 8
4x - 12y = -36
Add the equations together:
(6x - 10y) + (4x - 12y) = 8 + (-36)
10x - 22y = -28
Solve this equation for x:
x = (10x - 22y + 28)/10
x = 2.2y - 2.8
Substitute x back into 3x - 5y = 4:
3(2.2y - 2.8) - 5y = 4
6.6y - 8.4 - 5y = 4
1.6y - 8.4 = 4
1.6y = 12.4
y = 7.75
Substitute y back into x = 2.2y - 2.8:
x = 2.2(7.75) - 2.8
x = 17.05
Therefore, the solution to the system of equations is x = 17.05 and y = 7.75.