Question

Solve the system using linear combinations.
–5x + y = 1
9x – 2y = 4

Answer 1

Multiply first equation with 2. Then add first and second, we get -x=6. X=-6 and y=-29

Answer 2

(-6, -29)

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

Equality Properties

Algebra I

• Solving systems of equations using substitution/elimination

Explanation:

Step 1: Define Systems

-5x + y = 1

9x - 2y = 4

Step 2: Rewrite Systems

-5x + y = 1

1. Add 5x on both sides: y = 5x + 1

Step 3: Redefine Systems

y = 5x + 1

9x - 2y = 4

Step 4: Solve for x

Substitution

1. Substitute in y: 9x - 2(5x + 1) = 4
2. Distribute -2: 9x - 10x - 2 = 4
3. Combine like terms: -x - 2 = 4
4. Isolate x term: -x = 6
5. Isolate x: x = -6

Step 5: Solve for y

1. Define equation: -5x + y = 1
2. Substitute in x: -5(-6) + y = 1
3. Multiply: 30 + y = 1
4. Isolate y: y = -29