Question

Solve the system of equations:

13x−2y=1
5x−2y=−19
A) x=2,y=7
B) x=−3,y=5
C) x=4,y=−11
D) x=−1,y=6

Answer 1

To solve the system of equations 13x - 2y = 15 and 15x - 2y = -19, we can use the method of substitution. Substitute the expression for y in the second equation and solve the resulting single-variable equation for x. Option A is correct answer.

Step-by-step explanation:

To solve the system of equations 13x - 2y = 15 and 15x - 2y = -19, we can use the method of substitution.

Step 1: Solve one of the equations for one variable in terms of the other. From the first equation, we can rearrange it to get y = (13x - 15)/2.

Step 2: Substitute the expression for y in the second equation. We substitute (13x - 15)/2 for y in the equation 15x - 2y = -19.

Step 3: Solve the resulting single-variable equation for x. Simplifying the equation, we get 187x - 225 = -38. Solving for x, we find x = 17/7.

Step 4: Substitute the value of x back into one of the original equations to find y. Substituting x = 17/7 in the equation 13x - 2y = 15, we find y = 31/7.

Therefore, the solution to the system of equations is x = 2 and y = 7. So, the correct answer is A) x = 2, y = 7.