solve by the elimination method
x+4y=17
-x+6y=3
What is the solution of the system?
the solution is ______
there are infinitely many solutions ___
or there is no solution?______
To solve the system of equations by the elimination method, we need to eliminate one variable by manipulating the two equations. Let's solve the given system step by step:
Step 1: Add the two equations together. When we add them, the x-term in one equation will cancel out with the -x term in the other equation, leaving us with only the y-term.
(x + 4y) + (-x + 6y) = 17 + 3
4y + 6y = 17 + 3
10y = 20
Step 2: Divide both sides of the equation by 10 to solve for y:
10y/10 = 20/10
y = 2
Now that we have the value of y, we can substitute it back into either of the original equations to solve for x. Let's use the first equation:
x + 4(2) = 17
x + 8 = 17
x = 17 - 8
x = 9
So the solution to the system of equations is x = 9 and y = 2.
Based on the given equations, there is a unique solution (9, 2) to this system.