solve the system using elimination
2x-5y=8
x-3y=-1
please explian step by step
To solve the system of equations using elimination, we want to eliminate one of the variables so that we can solve for the other variable. Let's start by eliminating the variable "x" in this case.
Step 1: Multiply both sides of the second equation by 2 to make the coefficients of "x" the same in both equations.
2 * (x - 3y) = 2 * (-1)
2x - 6y = -2
Now, the system of equations looks like this:
2x - 5y = 8
2x - 6y = -2
Step 2: Subtract the first equation from the second equation.
(2x - 6y) - (2x - 5y) = (-2) - 8
2x - 6y - 2x + 5y = -10
Simplifying we get:
-y = -10
Step 3: Multiply both sides of the equation by -1 to solve for "y".
(-y) * (-1) = (-10) * (-1)
y = 10
Step 4: Substitute the value of "y" back into one of the original equations to solve for "x". Let's use the first equation:
2x - 5(10) = 8
2x - 50 = 8
Step 5: Add 50 to both sides of the equation.
2x - 50 + 50 = 8 + 50
2x = 58
Step 6: Divide both sides of the equation by 2 to solve for "x".
(2x)/2 = 58/2
x = 29
Therefore, the solution to the system of equations is:
x = 29
y = 10
double eq #2 and you have
2x-5y = 8
2x-6y = -2
Now subtract #2 from #1 and you eliminate x:
y = 10
Now you can use either equation to find x.
first equation: 2x - 5y = 8
double the 2nd: 2x - 6y = -2
subtract them:
y = 10
back into the original 2nd
x - 3y = -1
x - 30 = -1
x = 29
x = 29, y = 10