Use addition or substitution to find the value of y for this set of equations.
4x + 13y = 40
4x + 3y = -40
I would subtract them to get
10y = 80
y = 8
back into the second:
4x + 24 = -40
4x = -64
x = -16
Use addition or substitution to find the value of x for this set of equations.
2x - 3y = -15
x = 4y
To find the value of y for this set of equations, we can use either the addition or substitution method.
Let's start with the addition method:
Step 1: Multiply one or both of the equations by a suitable factor to make the coefficients of x or y in both equations the same (or opposites).
In this case, we can achieve this by multiplying the second equation by -4:
Original equations:
4x + 13y = 40
4x + 3y = -40
Multiplying the second equation by -4:
-4(4x + 3y) = -4(-40)
-16x - 12y = 160
Step 2: Add the two equations together, eliminating either x or y.
Adding the modified second equation (-16x - 12y = 160) to the first equation (4x + 13y = 40), we get:
(4x + 13y) + (-16x - 12y) = 40 + 160
Simplifying the equation:
-12x + y = 200
Now we have a new equation: -12x + y = 200
Step 3: Isolate the variable of interest.
To find the value of y, we need to isolate it on one side of the equation. Let's move -12x to the other side:
y = 200 + 12x
So, the value of y is 200 + 12x.
Alternatively, we can use the substitution method to find the value of y:
Step 1: Solve one of the equations for either x or y (preferably one of the equations that already has one of the variables isolated).
In this case, let's solve the second equation (4x + 3y = -40) for x:
4x = -40 - 3y
x = (-40 - 3y)/4
Step 2: Substitute the expression obtained for x in one of the original equations and solve for y.
We will substitute x with (-40 - 3y)/4 in the first equation (4x + 13y = 40):
4((-40 - 3y)/4) + 13y = 40
-40 - 3y + 13y = 40
Simplifying the equation:
-40 + 10y = 40
Step 3: Solve for y.
Adding 40 to both sides of the equation:
-40 + 40 + 10y = 40 + 40
10y = 80
Dividing both sides by 10:
y = 8
So, the value of y is 8.
Using either the addition or substitution method, we find that the value of y is 8.