Maths-

General

Easy

Question

# Solve the system of equations by elimination :

X - 2Y = 1

2X + 3Y= - 12

Hint:

**HINT:** Perform any arithmetic operation and then find.

## The correct answer is: x = - 3 and y = - 2

### Complete step by step solution:

Let x - 2y = 1…(i)

and 2x + 3y=-12….(ii)

On multiplying (i) with 2, we get 2(x - 2y = 1)

⇒ 2x - 4y = 2…(iii)

Now, we have the coefficients of x in (ii) and (iii) to be the same.

On subtracting (ii) from (iii),

we get LHS to be 2x - 4y - (2x + 3y) = - 4y - 3y = - 7y

and RHS to be 2 - (- 12) = 14

On equating LHS and RHS, we have - 7y = 14

⇒ y = - 2

On substituting the value of y in (i), we get x - 2 × - 2 =1

⇒ x + 4 = 1

⇒ x = 1-4

⇒ x = - 3

Hence we get x = - 3 and y = - 2

Note: We can also solve these system of equations by making the coefficients of y

to be the same in both the equations

### Related Questions to study

Maths-

### Solve the equation. Write a reason for each step.

𝑥 − 2 + 3(𝑥 + 2) = 3𝑥 + 10

### Solve the equation. Write a reason for each step.

𝑥 − 2 + 3(𝑥 + 2) = 3𝑥 + 10

Maths-General

Maths-

### Use Substitution to solve each system of equations :

6X - 3Y = -6

Y = 2X + 2

### Use Substitution to solve each system of equations :

6X - 3Y = -6

Y = 2X + 2

Maths-General

Maths-

### Given: 𝑚∠𝑃 = 30°, 𝑚∠𝑄 = 30° , 𝑚∠𝑄 = 𝑚∠𝑅

Prove: 𝑚∠𝑃 ≅ 𝑚∠𝑅 = 30°

### Given: 𝑚∠𝑃 = 30°, 𝑚∠𝑄 = 30° , 𝑚∠𝑄 = 𝑚∠𝑅

Prove: 𝑚∠𝑃 ≅ 𝑚∠𝑅 = 30°

Maths-General

Maths-

### Use the given information and the diagram to prove the statement.

Given: 𝑚∠𝑃𝑀𝐶 + 𝑚∠𝑃𝑀𝐷 = 180° and 𝑚∠𝑃𝑀𝐶 = 150°

Prove: 𝑚∠𝑃𝑀𝐷 = 30°

### Use the given information and the diagram to prove the statement.

Given: 𝑚∠𝑃𝑀𝐶 + 𝑚∠𝑃𝑀𝐷 = 180° and 𝑚∠𝑃𝑀𝐶 = 150°

Prove: 𝑚∠𝑃𝑀𝐷 = 30°

Maths-General

Maths-

### Solve the system of equations by elimination :

3X + 2Y = 8

X + 4Y = - 4

### Solve the system of equations by elimination :

3X + 2Y = 8

X + 4Y = - 4

Maths-General

Maths-

### Give a two-column proof.

Given:

Prove: PR = 25 in

### Give a two-column proof.

Given:

Prove: PR = 25 in

Maths-General

Maths-

### Use Substitution to solve each system of equations :

- 3X - Y = 7

X + 2Y = 6

### Use Substitution to solve each system of equations :

- 3X - Y = 7

X + 2Y = 6

Maths-General

Maths-

### If Q is the midpoint of PR, prove that PR = 2 PQ.

Give a two-column proof.

### If Q is the midpoint of PR, prove that PR = 2 PQ.

Give a two-column proof.

Maths-General

Maths-

### Compare 𝑚∠𝑃𝑂𝑄𝑎𝑛𝑑∠𝑆𝑂𝑇.

### Compare 𝑚∠𝑃𝑂𝑄𝑎𝑛𝑑∠𝑆𝑂𝑇.

Maths-General

Maths-

### Which postulate will you use to prove that PR = PQ + QR?

### Which postulate will you use to prove that PR = PQ + QR?

Maths-General

Maths-

### Solve the system of equations by elimination :

X - 2Y = - 2

3X + 2Y = 30

### Solve the system of equations by elimination :

X - 2Y = - 2

3X + 2Y = 30

Maths-General

Maths-

### Solve the following by using the method of substitution

Y = 4X+2

Y = X+8

### Solve the following by using the method of substitution

Y = 4X+2

Y = X+8

Maths-General

Maths-

### If lines l and m are parallel, find the value of x.

### If lines l and m are parallel, find the value of x.

Maths-General

Maths-

Prove that: PR = PQ + QR

Give a two-column proof

Prove that: PR = PQ + QR

Give a two-column proof

Maths-General

Maths-

### Find x and hence find 𝑚∠𝐶𝑂𝐷

### Find x and hence find 𝑚∠𝐶𝑂𝐷

Maths-General