Question

What is the x-value in the solution to this system of linear equations?

2x − y = 11

x + 3y = −5

−3
−1
2
4

Answer 1

x = 4

Explanation:

2x - y = 11

x + 3y = -5

To calculate the value of x , firstly we need to find value of y.

solve for y

• 2x - y = 11

subtract 2x from both side

• 2x - 2x - y = 11 - 2x
• -y = 11 - 2x

change the sign of both side of equation

• y = -11 + 2x

rewrite

• y = 2x - 11

Solve for x

• y = 2x - 11
• x + 3y = -5

substitute the value of y in the equation

• x + 3( 2x - 11 ) = -5

distribute 3

• x + 3 × 2x - 3× 11 = -5
• x + 6x - 33 = -5

combine like terms

• 7x - 33 = -5

Add 33 on both side

• 7x - 33 + 33 = -5 + 33
• 7x = 28

divide both side by 7

• 7x / 7 = 28 / 7
• x = 4

Answer 2

4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Distributive Property

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Algebra I

• Terms/Coefficients
• Solving systems of equations using substitution/elimination

Explanation:

Step 1: Define Systems

2x - y = 11

x + 3y = -5

Step 2: Rewrite Systems

2x - y = 11

1. [Subtraction Property of Equality] Subtract 2x on both sides: -y = 11 - 2x
2. [Division Property of Equality] Divide -1 on both sides: y = 2x - 11

Step 3: Redefine Systems

y = 2x - 11

x + 3y = -5

Step 2: Solve for x

Substitution

1. Substitute in y [2nd Equation]: x + 3(2x - 11) = -5
2. [Distributive Property] Distribute 3: x + 6x - 33 = -5
3. Combine like terms: 7x - 33 = -5
4. [Addition Property of Equality] Add 33 on both sides: 7x = 28
5. [Division Property of Equality] Divide 7 on both sides: x = 4