Question
solve the system with elimination 2x+7y=17 and x-4y=-14
Answers
GPT 3.5
To solve the system using elimination, we can multiply both sides of the second equation by 2 to make the coefficients of x the same:
2(x - 4y) = 2(-14)
2x - 8y = -28
Now, the system becomes:
2x + 7y = 17
2x - 8y = -28
We can eliminate x by subtracting the second equation from the first equation:
(2x + 7y) - (2x - 8y) = 17 - (-28)
2x + 7y - 2x + 8y = 17 + 28
15y = 45
y = 3
Substituting the value of y back into one of the original equations, we can solve for x:
x - 4(3) = -14
x - 12 = -14
x = -14 + 12
x = -2
Therefore, the solution to the system of equations is x = -2 and y = 3.
2(x - 4y) = 2(-14)
2x - 8y = -28
Now, the system becomes:
2x + 7y = 17
2x - 8y = -28
We can eliminate x by subtracting the second equation from the first equation:
(2x + 7y) - (2x - 8y) = 17 - (-28)
2x + 7y - 2x + 8y = 17 + 28
15y = 45
y = 3
Substituting the value of y back into one of the original equations, we can solve for x:
x - 4(3) = -14
x - 12 = -14
x = -14 + 12
x = -2
Therefore, the solution to the system of equations is x = -2 and y = 3.