4x+5y = 11 and 2x+6y = 16
Let's start by solving 4x+5y = 11 for the variable x.
Move the 5y to the right hand side by subtracting 5y from both sides, like this:
From the left hand side:
5y - 5y = 0
The answer is 4x
From the right hand side:
The answer is 11-5y
Now, the equation reads:
4x = 11-5y
To isolate the x, we have to divide both sides of the equation by theother variables
around the x on the left side of the equation.
The last step is to divide both sides of the equation by 4 like this:
To divide x by 1
The x just gets copied along in the numerator.The answer is x4x ÷ 4 = x
To divide 11-5y by 4divide each term in 11-5y by 4 term by term.11 ÷ 4 =11/4
To divide y by 1
The y just gets copied along in the numerator.-5y ÷ 4 =The solution to your equation is:
x =Next, let's solve 2x+6y = 16 for the variable y.
Move the 2x to the right hand side by subtracting 2x from both sides, like this:
From the left hand side:
2x - 2x = 0The answer is 6yFrom the right hand side:
The answer is 16-2x
Now, the equation reads:
6y = 16-2x
To isolate the y, we have to divide both sides of the equation by theother variables
around the y on the left side of the equation.
The last step is to divide both sides of the equation by 6 like this:
To divide y by 1The y just gets copied along in the numerator.The answer is y6y ÷ 6 = yTo divide 16-2x by 6divide each term in 16-2x by 6 term by term.16 ÷ 6 =To divide x by 1The x just gets copied along in the numerator.-2x ÷ 6 =The solution to your equation is:
y =Now, plug the earlier result, x=11/4-5/4y, in for x everywhere it occurs in
y=8/3-1/3x.
This gives y=8/3-1/3(11/4-5/4y). Now all we have to do is solve this for y,to have our first solution.
8/3 evaluates to 1/3 evaluates to 11/4 evaluates to 5/4 evaluates to Multiply y andMultiply y and 1The y just gets copied along.The answer is yy5/4*y evaluates to 11/4-5/4*y evaluates to Multiply bywe multiply by each term in term by term.This is the distributive property of multiplication.Multiply and1 × =Multiply andMultiply 1 and yThe y just gets copied along.y × =1/3*(11/4-5/4*y) evaluates to - =The answer is8/3-1/3*(11/4-5/4*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 isFrom the right hand side:
- = 0The answer is
Now, the equation reads:
=
To isolate the y, we have to divide both sides of the equation by theother 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 1The y just gets copied along in the numerator.The answer is y ÷ = y ÷ = 3The solution to your equation is:
y = 3Lastly, to find the solution for x, we plug this answer for y into the earlier result that
x=11/4-5/4y.
This gives x=11/4-5/4(3). Now, simplify this.
11/4 evaluates to 5/4 evaluates to Multiply and 315/4*(3) evaluates to 11/4-5/4*(3) evaluates to -1x= -1So, the solutions to your equations are:
x= -1 and y= 3The answer is xThe answer is y
