Mathematics

Grade10

Easy

Question

# Solve the system:

y = -2x + 3

4x + 2y = 12

- No solution
- (5, 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 + 3 and 4x + 2y = 12

So we can write,

y = -2x + 3 …(i)

4x + 2y = 12 …(ii)

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

4x + 2(-2x + 3) = 12

4x – 4x + 6 = 12

6 = 12

The statement 6 = 12 is false, so the system of equations has no solution.

Therefore the system of equation of 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.