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Answer:
x = 3 and y = -1
Step-by-step explanation:
The problem to solve is:
The goal here is to solve
37x+41y=70 and
41x+37y=86 for the variables x and y.
First, let's work on your first equation,37x+41y=70
This means, see if it can be simplified at all before attempting to solve it.
Multiply x and 37
Multiply x and 1
The x just gets copied along.
The answer is x
x
37*x evaluates to 37x
Multiply y and 41
Multiply y and 1
The y just gets copied along.
The answer is y
y
41*y evaluates to 41y
37*x+41*y evaluates to 37x+41y
So, all-in-all, your first equation can be written as: 37x+41y = 70
Now, let's work on your second equation,41x+37y=86 Multiply x and 41
Multiply x and 1
The x just gets copied along.
The answer is x
x
41*x evaluates to 41x
Multiply y and 37
Multiply y and 1
The y just gets copied along.
The answer is y
y
37*y evaluates to 37y
41*x+37*y evaluates to 41x+37y
So, all-in-all, your second equation can be written as: 41x+37y = 86
After this initial survey of the equations, the system of equations we'll set out to solve is:
37x+41y = 70 and 41x+37y = 86
Let's start by solving 37x+41y = 70 for the variable x.
Move the 41y to the right hand side by subtracting 41y from both sides, like this:
From the left hand side:
41y - 41y = 0
The answer is 37x
From the right hand side:
The answer is 70-41y
Now, the equation reads:
37x = 70-41y
To isolate the x, we have to divide both sides of the equation by the other variables
around the x on the left side of the equation.
The last step is to divide both sides of the equation by 37 like this:
To divide x by 1
The x just gets copied along in the numerator.
The answer is x
37x ÷ 37 = x
To divide 70-41y by 37
divide each term in 70-41y by 37 term by term.
70 ÷ 37 =
To divide y by 1
The y just gets copied along in the numerator.
The answer is y
-41y ÷ 37 =
The solution to your equation is:
x =
Next, let's solve 41x+37y = 86 for the variable y.
Move the 41x to the right hand side by subtracting 41x from both sides, like this:
From the left hand side:
41x - 41x = 0
The answer is 37y
From the right hand side:
The answer is 86-41x
Now, the equation reads:
37y = 86-41x
To isolate the y, we have to divide both sides of the equation by the other variables
around the y on the left side of the equation.
The last step is to divide both sides of the equation by 37 like this:
To divide y by 1
The y just gets copied along in the numerator.
The answer is y
37y ÷ 37 = y
To divide 86-41x by 37
divide each term in 86-41x by 37 term by term.
86 ÷ 37 =
To divide x by 1
The x just gets copied along in the numerator.
The answer is x
-41x ÷ 37 =
The solution to your equation is:
y =
Now, plug the earlier result, x=70/37-41/37y, in for x everywhere it occurs in
y=86/37-41/37x.
This gives y=86/37-41/37(70/37-41/37y). Now all we have to do is solve this for y,to have our first solution.
86/37 evaluates to
41/37 evaluates to
70/37 evaluates to
41/37 evaluates to
Multiply y and
Multiply y and 1
The y just gets copied along.
The answer is y
y
41/37*y evaluates to
70/37-41/37*y evaluates to
Multiply by
we multiply by each term in term by term.
This is the distributive property of multiplication.
Multiply and
1
× =
Multiply and
Multiply 1 and y
The y just gets copied along.
y
× =
41/37*(70/37-41/37*y) evaluates to
- =
The answer is
86/37-41/37*(70/37-41/37*y) evaluates to
Move the to the left hand side by subtracting from both sides, like this:
From the left hand side:
y - =
The answer is
From the right hand side:
- = 0
The answer is
Now, the equation reads:
=
To isolate the y, we have to divide both sides of the equation by the other variables
around the y on the left side of the equation.
The last step is to divide both sides of the equation by like this:
To divide y by 1
The y just gets copied along in the numerator.
The answer is y
÷ = y
÷ = -1
The solution to your equation is:
y = -1
Lastly, to find the solution for x, we plug this answer for y into the earlier result that
x=70/37-41/37y.
This gives x=70/37-41/37(-1). Now, simplify this.
70/37 evaluates to
41/37 evaluates to
Because of the minus sign
1 becomes - 1
The answer is -1
Multiply and -1
1
41/37*(-1) evaluates to
70/37-41/37*(-1) evaluates to 3
x= 3
So, the solutions to your equations are:
x= 3 and y= -1