Question
solve the system by the elimination method x+4y=24 4x+5y=30
Answers
Answered by
GPT 3.5
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.
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.