-3x+y=-5 x+2y=0
Your equations:
-3x + y = -5
x + 2y = 0
Let's solve the second equation for x:
x = -2y
Now let's substitute -2y for x in the first equation to solve for y:
-3(-2y) + y = -5
6y + y = -5
7y = -5
y = -5/7
Now let's substitute -5/7 for y in the second equation to solve for x:
x + 2(-5/7) = 0
x + -10/7 = 0
x = 10/7
Check these values with the original equations. It always helps to check your work!
I hope this will help.
To solve the system of equations -3x + y = -5 and x + 2y = 0, we can use the method of substitution.
First, let's solve the second equation for x. We can rewrite x + 2y = 0 as x = -2y.
Now, we substitute -2y for x in the first equation: -3(-2y) + y = -5.
Simplifying this equation, we get 6y + y = -5, which gives us 7y = -5.
Dividing both sides of the equation by 7, we find y = -5/7.
Now, let's substitute -5/7 for y in the second equation: x + 2(-5/7) = 0.
Simplifying this equation, we get x + (-10/7) = 0, which can be rewritten as x = 10/7.
So, the solution to the system of equations is x = 10/7 and y = -5/7.
To check these values, substitute them back into the original equations and see if they satisfy both equations.
In the first equation: -3(10/7) + (-5/7) = -5, we get -30/7 - 5/7 = -5, which simplifies to -35/7 = -5. This is true.
In the second equation: (10/7) + 2(-5/7) = 0, we get 10/7 - 10/7 = 0, which is also true.
Therefore, the values x = 10/7 and y = -5/7 satisfy both equations and are the solution to the system of equations.
I hope this explanation helps!