Answer:
Solution: x = 3, y = 2, or (3, 2)
Step-by-step explanation:
Given the systems of linear equations with two variables:
[tex]\displaystyle\mathsf{\left \{{Equation\:1:\:4x - 2y =\:8} \atop {Equation\:2:\:3x + 4y = 17}} \right}[/tex]
The process of elimination will be used to solve for the solution to the given problem.
Step 1:
First, we must multiply Equation 1 by 2:
(2)[4x - 2y] = 8(2)
8x - 4y = 16
Step 2:
Add the revised Equation 1 (from the previous step) to Equation 2:
[tex]\displaystyle\mathsf{\left \ {{\quad \:\:\:8x\:- 4y = 16} \atop + {\quad\underline {\:\:3x\:+ 4y = 17\:} \underline}} \right.}\\\displaystyle\mathsf{\qquad\:\:11x\qquad\:=33}[/tex]
Step 3:
Next, divide both sides by 11 to solve for x:
[tex]\displaystyle\mathsf{\frac{11x}{11}\:=\:\frac{33}{11}}[/tex]
x = 3
Step 4:
Substitute the value of x = 3 into Equation 1 to solve for y:
4x - 2y = 8
4(3) - 2y = 8
12 - 2y = 8
Step 5:
Subtract 12 from both sides:
12 - 12 - 2y = 8 - 12
- 2y = -4
Step 6:
Divide both sides by -2 to solve for y:
[tex]\displaystyle\mathsf{\frac{-2y}{-2}\:=\:\frac{-4}{-2} }[/tex]
y = 2
Double-check:
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).
