The set of equations 9x - 4y = -109 and 7x+89=y has to be solved for x and y.

Substitute y = 7x+89 in 9x - 4y = -109

=> 9x - 4(7x+89) = -109

=> 9x - 28x - 356 = -109

=> 19x = -247

=> x = -13

y = 7*(-13) + 89 = -2

**The solution of the set of equations is x = -13 and y = -2**

*Solve 9x-4y=-109 and 7x+89=y using the substitution method.

The substitution method is a technique used to solve a linear system of equations. Substitute the equation that has been solved for one of the variables into the other equation and solve for the other remaining variable value. Then use that variable value to solve for the value of the other remaining variable in the other equation.

First use the symmetric property to change the order of the equation 7x+89=y to y= 7x+89. Now substitute the value for y which is equal to 7x+89 into the other equation 9x-4y=-109. The equation becomes 9x-4(7x+89)=-109. Use the distributive property to distribute the -4 across the two addends 7x and 89. The equation becomes 9x-4x7x-4x89=-109.Use the multiplivative property to simplify this equation. The equation becomes 9x-28x-356=-109. Use the addition property to add 356 to both sides of the equation. The equation becomes 9x-28x=247. Subtract 28x from 9x in the equation. The equation becomes -19x=247. Use the division property to solve for x. The equation becomes x= -13. Now substitute the value for x into the equation y=7x+89 which has been solved for the y variable. The value of y can be found by substituting the value of x into this equation. The equation becomes y= 7x-13+89. Use the multiplicative property to find the product of 7x-13. The equation becomes y=-91+89. The equation becomes y=-2. The solution is the ordered pair is (-13,-2).

y= 7x+89

9x-4y=-109

9x-4(7x+89)=-109

9x-4*7x-4*89=-109

9x-28x-356=-109

9x-28x=247

-19x=247

-19x/-19=247/-19

x=-13

y=7x+89

y=7*-13+89

y=-91+89

y=-2

Check

Substitute the values for x and y into this equation 9x-4y=-109. The equation becomes 9x-13-4x-2=-109. Use the multiplicative property to find the product of 9x-13 and -4x-2. The equation becomes -117+8=-109. The equation becomes

-109=-109. This proves that the values found for x and y are correct.