I need a step by step explanation on how to add these two equations
2x+3y=1
5x+3y=16
Subtract the first equation from the second. (Subtract left and right sides separately). This gives you
3x = 15
Then divide both sides by 3.
x = 5
Pretty easy, huh?
After you have x, you can get y by using any of the original equations.
10 + 3y = 1
Subtract 10 from both sides.
3y = -9
Divide both sides by 3
y = -3
2x + 3y =1
5x + 3y = 16
Multiply the 2nd equation by -1, then add them together like this:
2x + 3y = 1
-5x - 3y =-16
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-3x = -15
Divide by -3 to get x =5. Now, substitute 5 for x in one of the equations and solve for y.
To add the two equations:
1. Write down the equations:
2x + 3y = 1
5x + 3y = 16
2. Look at the coefficients of the terms in front of the variables. In this case, the coefficients in front of y are the same in both equations.
3. Decide which method you want to use to eliminate one variable. Since the coefficients of y are the same, you can subtract the equations to eliminate y.
4. Subtract the first equation from the second equation. When subtracting, make sure to do it term by term. Subtract the left sides separately and subtract the right sides separately:
(5x + 3y) - (2x + 3y) = (16 - 1)
Simplify by canceling out the like terms:
5x - 2x + 3y - 3y = 16 - 1
Rewrite the equation:
3x = 15
So now you have an equation with only one variable.
5. Solve for x by dividing both sides of the equation by 3:
(3x)/3 = 15/3
Simplify:
x = 5
Now you have the value of x.
6. Substitute the value of x back into one of the original equations to solve for y. Let's use the first equation:
2(5) + 3y = 1
Simplify:
10 + 3y = 1
7. Solve for y by isolating y on one side of the equation. Subtract 10 from both sides:
3y = 1 - 10
Simplify:
3y = -9
8. Solve for y by dividing both sides by 3:
(3y)/3 = (-9)/3
Simplify:
y = -3
Now you have both x and y values that satisfy both equations.
Therefore, the solution to the system of equations is x = 5 and y = -3.