Mathematics

Grade10

Easy

Question

# Solve the system:

y = -2x + 20

2x + y = 10

- No solution
- (11, 8)
- (5, 15)
- Infinitely many solutions

Hint:

### In this question, we are given two system of equation , we have to find the value x and y. Make two equation , if (a1/a2) = (b1/b2) = (c1/c2) then it is infinitely many solutions, if (a1/a2) = (b1/b2) ≠ (c1/c2) and if (a1/a2) ≠(b1/b2) then it is unique solution.

## The correct answer is: No solution

### Here we have solve the system of equation and find x and y.

Firstly , we are given, y = -2x + 20 and 2x + y = 10

So we can write,

y = -2x + 20 -------( 1)

2x + y = 10 --------(2)

Now , we have a1/a2

a1/a2 = 2/2 =1

and b1/b2 ,

b1/b2 = 1/1 = 1

and c1/c2

c1/c2 = 20/10= 2

so here,

1 = 1 ≠ 2

a1/a2 = b1/b2 ≠ c1/c2

Therefore, the system of equation of no solution.

The correct answer is No solution.

Or Another way to solve the question,

y = -2x + 20 …(i)

2x + y = 10 …(ii)

Substituting y from (i) in (ii), we get

2x + (-2x + 20) = 10

20 = 10

The statement 20 = 10 is false, so the system of equations has no solution.

In this question, we have to find the system of equation. If (a1/a2) = (b1/b2) = (c1/c2) then it is infinitely many solutions, if (a1/a2) = (b1/b2) ≠ (c1/c2) and if (a1/a2) ≠(b1/b2) then it is unique solution.