Answer:
Solution: x = 3, y = 2, or (3, 2)
Step-by-step explanation:
Given the systems of linear equations with two variables:
![\displaystyle\mathsf{\left \{{Equation\:1:\:4x - 2y =\:8} \atop {Equation\:2:\:3x + 4y = 17}} \right}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cmathsf%7B%5Cleft%20%5C%7B%7BEquation%5C%3A1%3A%5C%3A4x%20-%202y%20%3D%5C%3A8%7D%20%5Catop%20%7BEquation%5C%3A2%3A%5C%3A3x%20%2B%204y%20%3D%2017%7D%7D%20%5Cright%7D)
The <u>process of elimination</u> will be used to solve for the solution to the given problem.
<h3><u /></h3><h3><u>Step 1:</u></h3>
First, we must multiply Equation 1 by 2:
(2)[4x - 2y] = 8(2)
8x - 4y = 16
<h3><u>Step 2:</u></h3>
Add the revised Equation 1 (from the previous step) to Equation 2:
![\displaystyle\mathsf{\left \ {{\quad \:\:\:8x\:- 4y = 16} \atop + {\quad\underline {\:\:3x\:+ 4y = 17\:} \underline}} \right.}\\\displaystyle\mathsf{\qquad\:\:11x\qquad\:=33}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cmathsf%7B%5Cleft%20%5C%20%7B%7B%5Cquad%20%5C%3A%5C%3A%5C%3A8x%5C%3A-%204y%20%3D%2016%7D%20%5Catop%20%2B%20%7B%5Cquad%5Cunderline%20%7B%5C%3A%5C%3A3x%5C%3A%2B%204y%20%3D%2017%5C%3A%7D%20%5Cunderline%7D%7D%20%5Cright.%7D%5C%5C%5Cdisplaystyle%5Cmathsf%7B%5Cqquad%5C%3A%5C%3A11x%5Cqquad%5C%3A%3D33%7D)
<h3><u>Step 3:</u></h3>
Next, divide both sides by 11 to solve for x:
x = 3
<h3><u>Step 4:</u></h3>
Substitute the value of x = 3 into Equation 1 to solve for y:
4x - 2y = 8
4(3) - 2y = 8
12 - 2y = 8
<h3><u>Step 5</u>: </h3>
Subtract 12 from both sides:
12 - 12 - 2y = 8 - 12
- 2y = -4
<h3><u>Step 6</u>: </h3>
Divide both sides by -2 to solve for y:
![\displaystyle\mathsf{\frac{-2y}{-2}\:=\:\frac{-4}{-2} }](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cmathsf%7B%5Cfrac%7B-2y%7D%7B-2%7D%5C%3A%3D%5C%3A%5Cfrac%7B-4%7D%7B-2%7D%20%7D)
y = 2
<h2><u>Double-check:</u></h2>
In order to verify whether we have the correct values for the solution, substitute x = 3, and y = 2 into both equations:
Equation 1: 4x - 2y = 8
4(3) - 2(2) = 8
12 - 4 = 8
8 = 8 (True statement).
Equation 2: 3x + 4y = 17
3(3) + 4(2) = 17
9 + 8 = 17
17 = 17 (True statement).
Therefore, the solution to the given system is x = 3, y = 2, or (3, 2).