Question

How do you solve this system of equations: \[-6x+6y=-12\] and \[-10x+9y=-17\]?

Answer 1

Hint: This question is from the topic of algebra. In this question, we will first make the equation \[-6x+6y=-12\] in simpler form. After that, we will solve both the equations and find out the value of x and y. We will use a substitution method to solve the further process of the solution of this question. We will take the value of x from the equation \[-6x+6y=-12\] and the value of x as in the equation \[-10x+9y=-17\]. After solving them, we will get our solution.

Complete step by step solution:
Let us solve this question.
In this question, we have to solve the system of equations. The equations are \[-6x+6y=-12\] and \[-10x+9y=-17\].
On dividing 6 to both sides of the equation \[-6x+6y=-12\] , we can write that equation as
\[\dfrac{-6x+6y}{6}=\dfrac{-12}{6}\]
We can write the above equation as
\[\Rightarrow -x+y=-2\]
The above equation can also be written as
\[\Rightarrow y=-2+x\]
Putting this value of y in the equation \[-10x+9y=-17\], we get
\[-10x+9\left( -2+x \right)=-17\]
The above equation can also be written as
\[\Rightarrow -10x-18+9x=-17\]
The above equation can also be written as
\[\Rightarrow -10x+9x=-17+18\]
The above equation can also be written as
\[\Rightarrow -x=1\]
The above equation can also be written as
\[\Rightarrow x=-1\]
Now, we will put this value of x as -1 in the equation \[-6x+6y=-12\], we will get
\[-6\left( -1 \right)+6y=-12\]
The above equation can also be written as
\[\Rightarrow 6+6y=-12\]
The above equation can also be written as
\[\Rightarrow y=\dfrac{-12-6}{6}=\dfrac{-18}{6}=-3\]
Hence, we get that the solutions to the system of equations are x=-1 and y=-3.

Note: As we can see that this question is from the topic of algebra. So, we should have a better knowledge in that topic. We have used a substitution method to solve this question. Always remember that in the substitution method, the value of one variable from one equation is substituted in that equation.