Question

Solve the system of equations.
3x−4y=40
5x−5y=55 (1 point)
Responses

(18, 7)
left parenthesis 18 comma 7 right parenthesis

(8,−3)
left parenthesis 8 comma negative 3 right parenthesis

(4,−7)
left parenthesis 4 comma negative 7 right parenthesis

(14, 3)
left parenthesis 14 comma 3 right parenthesis

Answer 1

To solve the system of equations, we can use the method of substitution or elimination.

Method of substitution:
From the first equation, we have 3x - 4y = 40. Solving for x, we get x = (40 + 4y)/3.

Substituting this into the second equation:
5((40 + 4y)/3) - 5y = 55.
Multiplying both sides by 3 to get rid of the fractions:
5(40 + 4y) - 15y = 165.
Expanding and simplifying:
200 + 20y - 15y = 165.
5y = 165 - 200.
5y = -35.
y = -35/5.
y = -7.

Substituting this value of y back into the first equation:
3x - 4(-7) = 40.
3x + 28 = 40.
3x = 40 - 28.
3x = 12.
x = 12/3.
x = 4.

Therefore, the solution to the system of equations is (4, -7).