The xy-value in the solution to the given system of linear equation shows that x = 2 and y = -4.
<h3>What is a system of linear equations?</h3>
Whenever two or more linear equations operate simultaneously, we create a System of Linear Equations. These equations must contain one or more similar variables in order to operate together.
When solving a system of linear equations, our objective is to simplify two equations having two variables to a single equation having one variable. Because each equation in the system includes two variables, substituting an expression for a variable is one technique to minimize the number of variables in an equation.
From the given information:
4x + 5y = -12 --- (1)
-2x + 3y = -16 ----- (2)
From equation (1)
4x+5y+(−5y) = −12 + (−5y) (Add -5y to both sides)
4x = −5y − 12
Divide both sides by 4
![\mathbf{\dfrac{4x}{4}= \dfrac{-5y-12}{4}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cdfrac%7B4x%7D%7B4%7D%3D%20%5Cdfrac%7B-5y-12%7D%7B4%7D%7D)
![\mathbf{x= \dfrac{-5}{4}y-3}](https://tex.z-dn.net/?f=%5Cmathbf%7Bx%3D%20%5Cdfrac%7B-5%7D%7B4%7Dy-3%7D)
Replacing the value of x in
into equation (2); we have:
![=\mathbf{-2(\dfrac{-5}{4}y-3)+3y=-16}](https://tex.z-dn.net/?f=%3D%5Cmathbf%7B-2%28%5Cdfrac%7B-5%7D%7B4%7Dy-3%29%2B3y%3D-16%7D)
![\mathbf{\dfrac{11}{2}y+6 =-16}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cdfrac%7B11%7D%7B2%7Dy%2B6%20%3D-16%7D)
Simplifying both sides of the equation, we have:
![\mathbf{\dfrac{11}{2}y+6-6 =-16-6}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cdfrac%7B11%7D%7B2%7Dy%2B6-6%20%3D-16-6%7D)
![\mathbf{\dfrac{11}{2}y=-22}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cdfrac%7B11%7D%7B2%7Dy%3D-22%7D)
Cross multiply
11y = -44
y = -4
Replace the value of y = -4 into ![\mathbf{x= \dfrac{-5}{4}y-3}](https://tex.z-dn.net/?f=%5Cmathbf%7Bx%3D%20%5Cdfrac%7B-5%7D%7B4%7Dy-3%7D)
![\mathbf{x= \dfrac{-5}{4}(-4)-3}](https://tex.z-dn.net/?f=%5Cmathbf%7Bx%3D%20%5Cdfrac%7B-5%7D%7B4%7D%28-4%29-3%7D)
x = 2
Learn more about systems of linear equations here:
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Answer:
20
Step-by-step explanation:
The ratio is 3:5, so 3x4 equals 12, then 5x4=20.
The length is 7, check the comments to see my progress to my solution.
Answer:
140/3
Step-by-step explanation:
(28/3)*5
140/3