Mathematics

Grade10

Easy

Question

# Solve the system:

y = 3x + 15

3x – y = -4

- 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 = 3x + 15 and 3x – y = -4

So we can write,

y= 3x +15

3x – y = -15 -------( 1)

3x – y = -4 --------(2)

Now , we have a1/a2

a1/a2 = 3/3 =1

and b1/b2 ,

b1/b2 = -1/-1 = 1

and c1/c2

c1/c2 = (-15)/(-4)= 15/4

so here,

1 = 1 ≠ 15/4

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.

y = 3x + 15 …(i)

3x – y = -4 …(ii)

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

3x – (3x + 15) = -4

15 = -4

The statement 15 = –4 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.