At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
Answer:
x=-4, y=8 and z=-1.
Explanation:
Given the system of equations:
[tex]\begin{gathered} 2x+3y+2z=14 \\ -3x+2y+z=27 \\ 4x+5y-4z=28 \end{gathered}[/tex]Step 1: Make z the subject in the second equation.
[tex]\begin{gathered} -3x+2y+z=27 \\ z=27+3x-2y \end{gathered}[/tex]Step 2: Substitute z into the first and third equations.
First equation
[tex]\begin{gathered} 2x+3y+2z=14 \\ 2x+3y+2(27+3x-2y)=14 \\ 2x+3y+54+6x-4y=14 \\ 2x+6x+3y-4y=14-54 \\ 8x-y=-40 \\ \implies y=8x+40 \end{gathered}[/tex]Third equation
[tex]\begin{gathered} 4x+5y-4z=28 \\ 4x+5y-4(27+3x-2y)=28 \\ 4x+5y-108-12x+8y=28 \\ 4x-12x+5y+8y=28+108 \\ -8x+13y=136 \end{gathered}[/tex]Step 4: Substitute y=8x+40 (first equation) into -8x+13y=136 (third equation).
[tex]\begin{gathered} -8x+13y=136 \\ -8x+13(8x+40)=136 \\ -8x+104x+520=136 \\ 96x=136-520 \\ 96x=-384 \\ x=-\frac{384}{96} \\ x=-4 \end{gathered}[/tex]Step 5: Solve for y
[tex]\begin{gathered} y=8x+40 \\ =8(-4)+40 \\ =-32+40 \\ y=8 \end{gathered}[/tex]Step 6: Solve for z.
[tex]\begin{gathered} z=27+3x-2y \\ =27+3(-4)-2(8) \\ =27-12-16 \\ z=-1 \end{gathered}[/tex]The solution to the system of equations is:
• x=-4
,• y=8; and
,• z=-1.
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.
