Question

Solve the following system of equations:

x = 40 + 3y
6x + 13y = 550

(5, 55)
(10, 70)
(70, 10)
(100, 20)

Answer 1

Solving the system of equations by substitution, the solution is found to be x = 70 and y = 10, corresponding to the option (70, 10).

Step-by-step explanation:

To solve the system of equations given in the question, we substitute the value of x from the first equation into the second equation and solve for y:

• x = 40 + 3y
• 6x + 13y = 550

Substitute x in the second equation:

1. 6(40 + 3y) + 13y = 550
2. 240 + 18y + 13y = 550
3. 31y + 240 = 550
4. 31y = 310
5. y = 10

Once we have the value of y, we can substitute it back into the first equation to find x:

1. x = 40 + 3(10)
2. x = 40 + 30
3. x = 70

Hence the solution to the system is x = 70 and y = 10, which corresponds to option (70, 10).

Answer 2

(10, 70)

Change the top equation to x-3y=40. Then multiply each value in that equation by 6 to make it 6x-18y=240. Then subtract each value. You should be left with -31y = -310, making y=10.