Question

(08.01 LC)

Two lines, A and B, are represented by the equations given below:
Line A: x + y = 2
Line B: 2x + y = 4
Which statement is true about the solution to the set of equations? (5 points)
1) There are infinitely many solutions.
2) There are two solutions.
3) There is one solution.
4) There is no solution.

Answer 1

There is one solution.

Explanation:

Answer 2

(2, 0)

There is one solution

Explanation:

Given the set of equations

x+y = 2

2x+y = 4

Substract both equations

x - 2x = 2 - 4

-x = -2

Multiply thrugh by -1

-1(-x) = -1(-2)

x = 2

Substitute x = 2 into equation1 ;

From 1, x+y = 2

2 + y = 2

y = 2-2

y = 0

hence the solution to the system of equation is (2, 0). Hence there is only one solution