How to solve systems of equations: 4x+5y=11

2 answers:

8 0

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

Anastasy [175]3 years ago

5 0

4x+5y=11
2x+6y=16

2x=16-6y
x=8-3y

4(8-3y)+5y=11
32-12y+5y=11
-7y=-21
y=3

4x+5(3)=11
4x+15=11
4x=-4
x=-1
(-1,3)

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Line L passes through the points (1, 1) and (7, 8). What is the slope of a line that is perpendicular to line L?

asambeis [7]

When a line passes through the two points $(x_{1},y_{1}) and (x_{2},y_{2})$ , its slope is given by the formula $m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

In this question, a line L passes through the points $(1,1) and (7,8)$

So, its slope is given by $m=\frac{8-1}{7-1}$

$m=\frac{7}{6}$

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Since, the slope of the line L is $\frac{7}{6}$ , so the slope of the line which is perpendicular to the given line L is $\frac{-6}{7}$ as the product of $\frac{-6}{7} \times \frac{7}{6}=-1$ .