Answer:
The solution to the system of equations be:
[tex]x=3,\:y=-1[/tex]
Hece, option B is correct.
Step-by-step explanation:
Given the system of equations
[tex]\begin{bmatrix}x-3y=6\\ 2x+2y=4\end{bmatrix}[/tex]
Multiply x − 3y = 6 by 2: 2x-6y=12
[tex]\begin{bmatrix}2x-6y=12\\ 2x+2y=4\end{bmatrix}[/tex]
so
[tex]2x+2y=4[/tex]
[tex]-[/tex]
[tex]\underline{2x-6y=12}[/tex]
[tex]8y=-8[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}2x-6y=12\\ 8y=-8\end{bmatrix}[/tex]
Solve 8y = -8 for y
[tex]8y=-8[/tex]
Divide both sides by 8
[tex]\frac{8y}{8}=\frac{-8}{8}[/tex]
[tex]y=-1[/tex]
[tex]\mathrm{For\:}2x-6y=12\mathrm{\:plug\:in\:}y=-1[/tex]
[tex]2x-6\left(-1\right)=12[/tex]
[tex]2x+6=12[/tex]
subtract 6 from both sides
[tex]2x+6-6=12-6[/tex]
[tex]2x=6[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}=\frac{6}{2}[/tex]
[tex]x=3[/tex]
Therefore, the solution to the system of equations be:
[tex]x=3,\:y=-1[/tex]
Hence, option B is correct.
⚽ From Equation (i) we get :
⚽ Now, Substitute the equation (iii) in equation (ii) we get :
→ 2(6 + 3y) + 2y = 4
→ 12 + 6y + 2y = 4
→ 8y = 4 - 12
→ 8y = -8
→ y = -8 ÷ 8
→ y = -1
⚽ Now Substituting value of y = -1 in equation (iii) we get :
→ x = 6 + 3y
→ x = 6 + 3(-1)
→ x = 6 + (-3)
→ x = 6 - 3
→ x = 3
