Solve by elimination: 5x+7y=77 , 5x+3y=53 can you please help me out step by step so I can understand it on my own, thanks.
-1(5x+7y=77 )
-5x -7y = -77
5x+3y=53
-4y = -24
y = 6
5x + 3(6) = 53
5x + 18 = 53
5x = 35
x = 7
3x+6y=6 2x-3y=4
hgyftgh
Certainly! To solve the given system of equations using elimination, follow these steps:
Step 1: Line up the two equations vertically so that the variables align.
5x + 7y = 77
5x + 3y = 53
Step 2: Multiply one or both of the equations by a constant so that the coefficients of one of the variables are the same (or differ by only a sign).
Since the coefficients of "x" are already the same in both equations, we won't need to multiply any of the equations by a constant.
Step 3: Choose one variable (either "x" or "y") and eliminate it by adding or subtracting the equations.
In this case, we will eliminate the variable "x". To do this, subtract the second equation from the first equation:
(5x + 7y) - (5x + 3y) = 77 - 53
This simplifies to:
4y = 24
Step 4: Solve for the eliminated variable.
Divide both sides of the equation by 4 to isolate "y":
4y/4 = 24/4
y = 6
So, we have found the value of "y" to be 6.
Step 5: Substitute the value of the eliminated variable back into one of the original equations to find the value of the remaining variable.
Let's substitute y = 6 into the first equation:
5x + 7(6) = 77
Simplifying further:
5x + 42 = 77
Step 6: Solve for the remaining variable.
Subtract 42 from both sides of the equation:
5x = 77 - 42
5x = 35
Divide both sides of the equation by 5 to isolate "x":
5x/5 = 35/5
x = 7
Therefore, the solution to the system of equations is x = 7 and y = 6.
The step-by-step explanation above should help you understand the process of solving the equations by elimination.