using the substitution method how do you solve y=-1/3x y+2x=5
y=(-1/3)x
y+2x=5
(-1/3)x+2x=5
(-1/3)x+(6/3)x=5
(5/3)x=5 Multiply with 3
5x=15 Divide with 5
x=15/5=3
y=(-1/3)x
y=(-1/3)*3= -1
x= 3 y= -1
To solve the given system of equations using the substitution method, we will first solve one equation for one variable and then substitute the expression obtained into the other equation.
Given equations:
1) y = -(1/3)x
2) y + 2x = 5
Step 1: Solve equation 1 for y
From equation 1, we have:
y = -(1/3)x
Step 2: Substitute equation 1 into equation 2
Replace y in equation 2 with -(1/3)x. So we get:
-(1/3)x + 2x = 5
Step 3: Solve equation 2 for x
Combine the like terms on the left side:
(2 - 1/3)x = 5
(6/3 - 1/3)x = 5
(5/3)x = 5
Step 4: Solve for x
To isolate x, we need to divide both sides of the equation by (5/3):
x = 5 / (5/3)
Step 5: Simplify
Dividing by a fraction is equivalent to multiplying by its reciprocal, so we have:
x = 5 * (3/5)
Simplifying, we get:
x = 3
Step 6: Find y
Now we substitute the value of x (which is 3) into either equation 1 or equation 2. Let's use equation 1:
y = -(1/3)(3)
y = -1
Step 7: Solution
The solution to the given system of equations is:
x = 3, y = -1
To solve the system of equations using the substitution method, follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation, y = (-1/3)x, for y.
We can multiply both sides by 3 to eliminate the fraction:
3y = -x
Step 2: Substitute the expression obtained in step 1 into the other equation.
Substitute -x for y in the second equation, y + 2x = 5.
-3x + 2x = 5
-x = 5
x = -5
Step 3: Substitute the value of x back into one of the original equations to find the value of y.
Let's substitute x = -5 into the first equation, y = (-1/3)x.
y = (-1/3)(-5)
y = 5/3
So, the solution to the system of equations is x = -5 and y = 5/3.