Question

How many solutions does the system have?
12 - 154 = 18
4x - 5y = 6 (1 point)

A. infinitely many solutions
B. two solutions
C. no solution
D. one solution

Answer 1

Solve the system of equations.
3x - 4y = 40
5x - 5y = 55 (1 point)
0 (8, -3)
O (4, -7)
O (14, 3)
O (18, 7)

Answer 2

The system of equations is:

Equation 1: 12 - 154 = 18
Equation 2: 4x - 5y = 6

Simplifying Equation 1, we get:

-142 = 18

This is not true. Therefore, the system of equations has no solution.

The answer is C. no solution.

Answer 3

To solve the system of equations, we can use the method of substitution or elimination. Here, let's use the method of substitution.

Given equations:

Equation 1: 3x - 4y = 40
Equation 2: 5x - 5y = 55

First, solve Equation 1 for x.

3x - 4y = 40
3x = 4y + 40
x = (4y + 40)/3

Now, substitute this value of x into Equation 2.

5x - 5y = 55
5((4y + 40)/3) - 5y = 55
(20y + 200)/3 - 5y = 55
20y + 200 - 15y = 165
5y + 200 = 165
5y = 165 - 200
5y = -35
y = -35/5
y = -7

Now, substitute this value of y into the equation we found for x.

x = (4(-7) + 40)/3
x = (-28 + 40)/3
x = 12/3
x = 4

The solution to the system of equations is x = 4 and y = -7.

The correct answer is O (4, -7).