Question

Solve the following system of equations.
-4x+9y=−13
5x+6y=-1
x=
y=​

Answer 1

x= 1 & y = -1

Explanation:

Since does not confirm which way you would prefer the question to be answered, I will be solving this system of equations using the method of substitution.

In order to find the values for the variables we will solve the equations individually and then substitute those answers into our equations until we isolate the variables completely.


`-4x+9y=-13`

`5x+6y=-1`
Solve -4x + 9y = -13:

`-4x+9y=-13`
Move 9y to the right side:

`-4x=-13+-9y`
Divide both sides by 4x:

`-4x/4x=x`

`x=(9)/(4) y+(13)/(4)`

Continue by substituting the value of x in the second equation:

`5x+6y=-1`

`5((9)/(4) y+(13)/(4))+6y=-1`
Simplify:

`5((9)/(4) y+(13)/(4))+6y=-1=(69)/(4) y+(65)/(4) =-1`

`(69)/(4) y+(65)/(4) =-1`
Add 65/4 on both sides:

`=(69)/(4) y+(65)/(4) =-1+(-65)/(4)`
Divide both sides by 69/4:

`(69)/(4)y /(69)/(4) =y`

`(-69)/(4) /(69)/(4) =-1`

`y=-1`
Substitute the value of y into the final equation:

`x=(9)/(4) y+(13)/(4)`

`x=(9)/(4) (-1)+(13)/(4)`
Now simplify one last time:

`x=(9)/(4) (-1)+(13)/(4)=1`

`x=1`

The value of x is 1 and the value of y is -1.

I hope this helps.