The solution to the system of equations is x= -7,y= -3.
When solving a system of equations using the substitution method, the goal is to find the values of the variables that satisfy both equations simultaneously. In this case, the system is represented by the equations:
−3x+4y=9
x−9y=20
To begin the substitution process, we isolate one of the variables in one of the equations. Let's choose the second equation x−9y=20. Solving for x: x=20+9y
Now that we have an expression for x, we substitute it into the first equation:
−3(20+9y)+4y=9
Next, we simplify and solve for y. After finding the value of y, we substitute it back into the expression we found for x:
x=20+9y
This process results in specific values for x and y. In this case, the solution is x=−7 and y=−3. These values satisfy both original equations, making them the solution to the given system. Therefore, the system of equations is solved using substitution, and the solution is x=−7,y=−3.