Answer:
(-5, 2)
Step-by-step explanation:
Given system of equations:
![\begin{cases}-2x-5y=20\\y=\dfrac{4}{5}x+2\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D-2x-5y%3D20%5C%5Cy%3D%5Cdfrac%7B4%7D%7B5%7Dx%2B2%5Cend%7Bcases%7D)
Both equations are linear equations.
<h3><u>Equation 1</u></h3>
Rearrange Equation 1 to make y the subject:
![\implies -2x-5y=20](https://tex.z-dn.net/?f=%5Cimplies%20-2x-5y%3D20)
![\implies -5y=2x+20](https://tex.z-dn.net/?f=%5Cimplies%20-5y%3D2x%2B20)
![\implies y=-\dfrac{2}{5}x-4](https://tex.z-dn.net/?f=%5Cimplies%20y%3D-%5Cdfrac%7B2%7D%7B5%7Dx-4)
Therefore, the graph of this equation is a straight line with a negative <u>slope</u> and a <u>y-intercept</u> of (0, -4).
Find two points on the line by substituting two values of x into the equation:
![x = 0\implies y=-\dfrac{2}{5}(0)-4=-4 \implies (0,-4)](https://tex.z-dn.net/?f=x%20%3D%200%5Cimplies%20y%3D-%5Cdfrac%7B2%7D%7B5%7D%280%29-4%3D-4%20%5Cimplies%20%280%2C-4%29)
![x = 5 \implies y=-\dfrac{2}{5}(5)-4=-6 \implies (5,-6)](https://tex.z-dn.net/?f=x%20%3D%205%20%5Cimplies%20y%3D-%5Cdfrac%7B2%7D%7B5%7D%285%29-4%3D-6%20%5Cimplies%20%285%2C-6%29)
Plot the found points and draw a straight line through them.
<h3><u>Equation 2</u></h3>
The graph of this equation is a straight line with a <u>positive slope</u> and a <u>y-intercept</u> of (0, 2).
Find two points on the line by substituting two values of x into the equation:
![x = 0 \implies y=\dfrac{4}{5}(0)+2=2 \implies (0,2)](https://tex.z-dn.net/?f=x%20%3D%200%20%5Cimplies%20y%3D%5Cdfrac%7B4%7D%7B5%7D%280%29%2B2%3D2%20%5Cimplies%20%280%2C2%29)
![x = 5 \implies y=\dfrac{4}{5}(5)+2=6 \implies (5,6)](https://tex.z-dn.net/?f=x%20%3D%205%20%5Cimplies%20y%3D%5Cdfrac%7B4%7D%7B5%7D%285%29%2B2%3D6%20%5Cimplies%20%285%2C6%29)
Plot the found points and draw a straight line through them.
<h3><u>Solution</u></h3>
The solution(s) to a system of equations is the <u>point(s) of intersection</u>.
From inspection of the graph, the point of intersection is (-5, -2).
To verify the solution, substitute the second equation into the first and solve for x:
![\implies \dfrac{4}{5}x+2=-\dfrac{2}{5}x-4](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B4%7D%7B5%7Dx%2B2%3D-%5Cdfrac%7B2%7D%7B5%7Dx-4)
![\implies \dfrac{6}{5}x=-6](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B6%7D%7B5%7Dx%3D-6)
![\implies 6x=-30](https://tex.z-dn.net/?f=%5Cimplies%206x%3D-30)
![\implies x=-5](https://tex.z-dn.net/?f=%5Cimplies%20x%3D-5)
Substitute the found value of x into one of the equations and solve for y:
![\implies \dfrac{4}{5}(-5)+2=-2](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B4%7D%7B5%7D%28-5%29%2B2%3D-2)
Hence verifying that (-5, -2) is the solution to the given system of equations.
Learn more about systems of equations here:
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