Question

6x-y= -23
8x+3y= -9
Solve by substitution method
Show work

Answer 1

x = - 3, y = 5

Explanation:

6x - y = - 23

8x + 3y = - 9

To solve a pair of equations using substitution first solve one of the equations of one of the variables. Then substitute the result in the other equation.

6x - y = - 23, 8x + 3y = - 9

Choose one of the equations and solve for x.

6x - y = - 23

Add y to both sides of the equation.

6x = y - 23

Divide both sides by 6.

x = 1/6 (y - 23)

Multiply 1/6 times y - 23.

x = 1/6y - 23/6

Substitute -23+y/6 for x in the other equation

8(1/6y - 23/6) + 3y = - 9

Multiply 8 times -23+y/6.

4/3y - 92/3 + 3y = - 9

Add 92/3 to both sides of the equation.

13/3y = 65/3

Divide both sides of the equation by 13/3y which is the same as multiplying both sides of the reciprocal of the fraction.

y = 5

Substitute 5 for y in x = 1/6y - 23/6 because the resulting equation contains only one variable, you can solve for x directly

x = 1/6(5) - 23/6

Multiply 1/6 times 5.

x = 5 - 23 / 6

Add -23/6 to 5/6 by finding a common denominator and adding the numerators. Then reduce the fraction to the lowest terms if possible.

x = - 3

The system is now solved.

x = - 3 , y = 5

Answer 2

(- 3, 5 )

Explanation:

6x - y = - 23 ( multiply through by - 1 )

- 6x + y = 23 (add 6x to both sides )

y = 23 + 6x → (1)

8x + 3y = - 9 → (2)

substitute y = 23 + 6x into (2)

8x + 3(23 + 6x) = - 9 ← distribute parenthesis and simplify left side

8x + 69 + 18x = - 9

26x + 69 = - 9 ( subtract 69 from both sides )

26x = - 78 ( divide both sides by 26 )

x = - 3

substitute x = - 3 into (1)

y = 23 + 6(- 3) = 23 - 18 = 5

solution is (- 3, 5 )