Solve the linear equation by elimination
10x-9y=46
-2x+3y=10
10x - 9y = 46
-10x + 15y = 30
6y = 96
y = 16
now get x from either equation
x=19 y=16
Well, well, well, looks like we've got ourselves a good old linear equation problem. Don't worry, I'm here to help with some elimination action!
First things first, let's multiply the second equation by 5 to make the coefficient of x the same in both equations:
-2x + 3y = 10 (Original Equation)
-10x + 15y = 50 (Multiply both sides by 5)
Now we've got a matching coefficient for x!
Next, let's add the two equations together:
(10x - 9y) + (-10x + 15y) = 46 + 50
Guess what? The magical elimination powers of clown math make the x-terms disappear!
-9y + 15y = 96
Now, let's combine like terms:
6y = 96
Finally, let's solve for y by dividing both sides by 6:
y = 16
Now that we have the value of y, we can substitute it back into any of the original equations, like the second one:
-2x + 3(16) = 10
Simplifying:
-2x + 48 = 10
Subtracting 48 from both sides:
-2x = -38
Dividing both sides by -2:
x = 19
So, the solution to the linear equations is x = 19, y = 16. Voila!
To solve the linear equations by elimination, we need to eliminate one of the variables by manipulating the equations. Let's start by getting rid of the x variable.
First, we'll multiply the second equation by 5 to make the coefficients of x in both equations the same:
-2x + 3y = 10 (Equation 1)
5(-2x + 3y) = 5(10) (Equation 2 multiplied by 5)
-10x + 15y = 50
Now, we have:
10x - 9y = 46 (Equation 3)
-10x + 15y = 50 (Equation 4)
Next, we'll add Equation 3 and Equation 4. This will eliminate the x variable since the coefficients of x are opposites:
(10x - 9y) + (-10x + 15y) = 46 + 50
Rearranging the terms, we get:
-9y + 15y = 96
Combining the like terms, we have:
6y = 96
To isolate y, we'll divide both sides of the equation by 6:
(6y)/6 = 96/6
Simplifying further, we get:
y = 16
Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's substitute it into Equation 1:
-2x + 3(16) = 10
Simplifying the equation, we have:
-2x + 48 = 10
Moving the constant term to the other side, we get:
-2x = 10 - 48
-2x = -38
Dividing by -2, we find:
x = -38 / -2
x = 19
Therefore, the solution to the system of equations is x = 19 and y = 16.
To solve the linear system of equations by elimination, follow these steps:
1. Multiply one or both equations by a constant(s) so that the coefficients of either x or y are equal or opposite in both equations. In this case, we'll multiply the second equation by 5 to make the coefficients of y equal in both equations.
Original equations:
Equation 1: 10x - 9y = 46
Equation 2: -2x + 3y = 10
Multiplying equation 2 by 5:
5*(-2x) + 5*(3y) = 5*10
-10x + 15y = 50
2. Now, add the two equations together term by term to eliminate one variable. The objective is to get a new equation with only one variable.
Adding the two equations together:
(10x - 9y) + (-10x + 15y) = 46 + 50
10x - 10x - 9y + 15y = 46 + 50
6y = 96
3. Solve the new equation with one variable, in this case, y.
6y = 96
Divide both sides by 6:
6y/6 = 96/6
y = 16
4. Substitute the value of y back into either of the original equations to solve for x. Let's use Equation 1:
10x - 9(16) = 46
10x - 144 = 46
10x = 46 + 144
10x = 190
Divide both sides by 10:
10x/10 = 190/10
x = 19
5. Therefore, the solution to the system of equations is x = 19 and y = 16.