solve the system by the elimination method x+4y=24 4x+5y=30
To solve the system of equations by the elimination method, we need to eliminate one variable by adding or subtracting the two equations.
1) Multiply the first equation by 4 to match the coefficients of x:
4(x + 4y) = 4(24)
4x + 16y = 96
2) Write down the second equation:
4x + 5y = 30
3) Subtract the second equation from the first equation:
(4x + 16y) - (4x + 5y) = 96 - 30
Simplifying:
11y = 66
4) Divide both sides of the equation by 11:
y = 6
5) Substitute the value of y into the first equation to solve for x:
x + 4(6) = 24
x + 24 = 24
x = 0
The solution to the system of equations is x = 0 and y = 6.