Question

Which of the following systems of equations has the solution (1,2)?

A. y−x=1
3y−4x=10

B. 3y−x=1
8y−2x=4

C. 3y+2x=8
4y−x=7

D. −2y+5x=−1
2y+2x=6

Answer 1

After substituting x=1 and y=2 into each equation of the provided systems, we find that only Option C satisfies both equations, making it the system with the solution (1,2).

Step-by-step explanation:

To find which of the following systems of equations has the solution (1,2), we need to substitute x with 1 and y with 2 into each equation of the systems provided. The correct system will satisfy both equations simultaneously with these values.

Let's plug in x=1 and y=2 into each equation:

A. 2−1=1 which is true and 3(2)−4(1)=10 which is false.
B. 3(2)−1=5 which is true and 8(2)−2(1)=14 which is false.
C. 3(2)+2(1)=8 which is true and 4(2)−1=7 which is true.
D. −2(2)+5(1)=1 which is false and 2(2)+2(1)=6 which is true.

Only Option C satisfies both equations with the solution (1,2).

Answer 2

C

Step-by-step explanation:

Plug in 1 for x and 2 for y in each equation. Your answer is the one where both equations are true.

3(2) + 2(1) = 8

6 + 2 = 8

8 = 8

4(2) - 1 = 7

8 - 1 = 7

7 = 7