solve the system of linear equations using the addition method. Can you please show me the steps on how you reached the answer. Thank You
2x+20y= -144
12x+5y= 56
In one equation, solve for one of the variables in terms of the other. For instance,
2x+20y=-144
2x=-144-20y
x=-72-10y
Then plug this variable into the other equation in order to yield a constant for y.
12(-72-10y)+5y=56
-864-120y+5y=56
-864-115y=56
-115y=920
y=-8.
But you're still not done. You have to plug this back into the equation in which you solved for x so you can get a constant value for x as well.
x=-72-10(-8)=-72+80=8
So x=8 and y=-8.
Please try a similiar problem like this on your own so you are able to fully understand how to go about solving systems of equations. This site is here to help you, not do your homework for you. You won't learn anything if you just copied what I just typed up. Learning comes best when cemented independently.
Good luck, and peace out.
To solve the system of linear equations using the addition method (also known as the elimination method), we need to eliminate one of the variables by adding or subtracting the equations.
Let's begin by eliminating one of the variables. Since the coefficients of y in the two equations are not the same, let's make them the same. To do this, we can multiply the first equation by 5 and the second equation by -20. This gives us:
Equation 1: 10x + 100y = -720
Equation 2: -240x - 100y = -1120
Now, let's add the two equations together to eliminate the y variable:
(10x + 100y) + (-240x - 100y) = -720 + (-1120)
Simplifying the equation:
10x - 240x + 100y - 100y = -720 - 1120
Combining like terms gives:
-230x = -1840
To solve for x, divide both sides of the equation by -230:
x = -1840 / -230
x = 8
Now substitute the value of x back into either of the original equations. Let's use Equation 1:
2x + 20y = -144
Substituting x = 8:
2(8) + 20y = -144
16 + 20y = -144
To solve for y, isolate the y term:
20y = -144 - 16
20y = -160
Divide both sides of the equation by 20:
y = -160 / 20
y = -8
Therefore, the solution to the system of linear equations is x = 8 and y = -8.