Question

Solve the System of Equations -4x + 9y = 14 12x - 10y = - 8

Answer 1

Answer:

(1, 2)

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

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtract Property of Equality

Algebra I

• Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

-4x + 9y = 14

12x - 10y = -8

Step 2: Rewrite Systems

-4x + 9y = 14

1. Multiply everything by 3:                    -12x + 27y = 42

Step 3: Redefine Systems

-12x + 27y = 42

12x - 10y = -8

Step 4: Solve for y

Elimination

1. Combine 2 equations:                    17y = 34
2. Divide 26 on both sides:                y = 2

Step 5: Solve for x

1. Define equation:                    12x - 10y = -8
2. Substitute in y:                       12x - 10(2) = -8
3. Multiply:                                  12x - 20 = -8
4. Isolate x term:                        12x = 12
5. Isolate x:                                 x = 1

Answer 2

Step-by-step explanation:

HERE,

two equation are,

●-4x+9y=14••••••••••••(equation I)

●12x-10y=-8•••••••••••(equation II)

First multiplying 3 in equation I

we get,

$\bold{3×(-4x+9y=14) }$

=$\bold{ -12x+27y=42 }$••(equation III)

Then,

we combine the equationii and equation III.

we get that,

$\bold{12x-10y-12x+27y=-8+42 }$

$\bold{\cancel{12x}-10y\cancel{-12x}+27y=-8+42 }$

$\rightsquigarrow$ $\bold{17y=34 }$

$\rightsquigarrow$ $\bold{ y=\dfrac{34}{17} }$

$\rightsquigarrow$ $\boxed{ y=2 }$

Then,

put the value of y in equation II.

WE get,

$\rightsquigarrow$ $\bold{12x-10×2=-8 }$

$\rightsquigarrow$ $\bold{ 12x-20=-8 }$

$\rightsquigarrow$ $\bold{ 12x=-8+20 }$

$\rightsquigarrow$ $\bold{ 12x=12 }$

$\rightsquigarrow$ $\bold{ x=\dfrac{12}{12} }$

$\rightsquigarrow$ $\boxed{ x=1 }$

So,

solution of the two equation (-4x+9y) and (12x-10y=-8) is (1,2)