Question

Solve the system of equations
-5X + 4Y = 3
X = 2Y - 15
X=
Y=

Answer 1

x = 9 and y = 12

Explanation:

-5x + 4y = 3

x = 2y - 15

We solve equation by using elimination method.

-5x + 4y = 3

x = 2y - 15

Solve for y.

Consider the second equation. Subtract 2y from both sides.

• x - 2y = - 15

In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

• -5x + 4y = 3, x - 2y = -15

To make -5x and x equal, multiply all terms on each side of the first equation by 1 and all terms on each side of the second by -5.

• 
  `\small \sf \: -5x+4y=3, \: \: \: -5x-5\left(-2\right)y=-5\left(-15\right)`

Simplify.

• -5x + 4y = 3, -5x + 10y = 75

Subtract -5x + 10y = 75 from -5x + 4y = 3 by subtracting like terms on each side of the equal sign.

• -5x + 5x + 4y - 10y = 3 - 75

Add -5x to 5x. Terms -5x and 5x cancel out, leaving an equation with only one variable that can be solved.

• 4y - 10y = 3 -75

combine like terms

• -6y = -72

Divide both side by -6

• -6y / -6 = -72/-6
• y = 12

Solve for x.

Plug 12 as y in first equation. Because the resulting equation contains only one variable, you can solve for x directly.

• -5x + 4 ( 12) = 3

Multiply 4 × 12 to get 48.

• -5x + 48 = 3

Subtract 48 from both sides.

• -5x + 48 - 48 = 3 - 48
• -5x = -45

Divide both sides of equation by -5

• -5x / -5 = -45/-5
• x = 9.

The system is now solved.

x = 9 and y = 12

Answer 2

x = 9

y = 12

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

-5x + 4y = 3

x = 2y - 15

Step 2: Solve for y

Substitution

1. Substitute in x [1st Equation]: -5(2y - 15) + 4y = 3
2. [Distributive Property] Distribute -5: -10y + 75 + 4y = 3
3. Combine like terms: -6y + 75 = 3
4. [Subtraction Property of Equality] Subtract 75 on both sides: -6y = -72
5. [Division Property of Equality] Divide -6 on both sides: y = 12

Step 3: Solve for x

1. Substitute in y [2nd Equation]: x = 2(12) - 15
2. Multiply: x = 24 - 15
3. Subtract: x = 9