menu

arrow_back Solve the simultaneous equations \(x+y=3\) and \(2 x^{2}+4 x y-y=15\)

by Gold Status
(30,445 points)
in Mathematics
22 views
Solve the simultaneous equations \(x+y=3\) and \(2 x^{2}+4 x y-y=15\)

1 Answer

Best answer
0 like 0 dislike
 
Best answer

\begin{array}{r}
x+y=3 \\
y=3-x \ldots \ldots \ldots \\
2 x^{2}+4 x y-y=15 \ldots \ldots \ldots . \\
\text { Substitute }(1) \text { into }(2): \\
2 x^{2}+4 x(3-x)-(3-x)=15 \\
2 x^{2}+12 x-4 x^{2}-3+x-15=0 \\
-2 x^{2}+13 x-18=0 \\
2 x^{2}-13 x+18=0 \\
(2 x-9)(x-2)=0 \\
x=\frac{9}{2} \quad \text { or } \quad x=2 \\
y=-\frac{3}{2} \text { or } \quad y=1
\end{array}

OR

\begin{gathered}
x+y=3 \\
x=3-y \ldots \ldots(1) \\
2 x^{2}+4 x y-y=15 \ldots \ldots \ldots(2) \\
\text { Substitute (1) into }(2): \\
2(3-y)^{2}+4(3-y) y-y=15 \\
2 y^{2}-12 y+18-4 y^{2}+12 y-y-15=0 \\
-2 y^{2}-y+3=0 \\
2 y^{2}+y-3=0 \\
(2 y+3)(y-1)=0 \\
y=-\frac{3}{2} \text { or } \quad y=1 \\
x=\frac{9}{2} \quad \text { or } \quad x=2
\end{gathered}

by Gold Status
(30,445 points)

Related questions


Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve the simultaneous equations: $\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2$ and $\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$
1 answer 124 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve the simultaneous equations: $3 x-y+z=5$; $2 x+2 y+3 z=4$ and $x+3 y-z=11$
1 answer 126 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Given the following simultaneous equations: $x+3 y=-1$ and $-3 x+6 y=8$, solve the given simultaneous equations by the substitution method.

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve simultaneous equations $y-3 x=5$ and $2 y+3 x=28$ by the method of elimination and substitution.
1 answer 95 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve the simultaneous equations $3x+y=8$ and $x+2 y=6$
1 answer 141 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve the simultaneous equations $a+b=4$ and $ 2 a+b=6$
1 answer 113 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve the simultaneous equation $4.9 x+1.5 y=38.3$ and $2.7 x-8.6 y=17.8$
1 answer 93 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve for $x$ in $5 x+3=28$
1 answer 81 views
Solve for $x$ in $5 x+3=28$Solve for $x$ in $5 x+3=28$ ...
by Maths Genie Bronze Status
(5,550 points)
asked in Mathematics Aug 12, 2021
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
$5(z+1)=3(z+2)+11$ Solve for $z$
1 answer 133 views
$5(z+1)=3(z+2)+11$ Solve for $z$$5(z+1)=3(z+2)+11$ Solve for $z$ ...
by MathsGee Platinum
(118,646 points)
asked in Mathematics Jul 22, 2021
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve the equation \( 8^{2 x-5}=2^{x+1} \)
1 answer 65 views
Solve the equation \( 8^{2 x-5}=2^{x+1} \)Solve the equation \( 8^{2 x-5}=2^{x+1} \) ...
by MathsGee Platinum
(118,646 points)
asked in Mathematics Nov 9, 2021
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve the system of equations by the Substitution Method. \[ \begin{aligned} &2 x-3 y=4 \\ &5 x+2 y=29 \end{aligned} \]
1 answer 195 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve the system of equations by the Elimination Method. \[ \begin{aligned} &0.1 x+0.3 y=1.4 \\ &9 x-3 y=-24 \end{aligned} \]
1 answer 158 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve the system of equations below with Gauss-Jordan elimination. \[ \begin{aligned} x+y-z &=10 \\ 2 x-y-z &=3 \\ -3 x-3 y+3 z &=-30 \end{aligned} \]

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve the system of equations by the Elimination Method. \[ \begin{aligned} &0.5 x-0.25 y=-0.5 \\ &-2 x+3 y=10 \end{aligned} \]
1 answer 166 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve the system of equations by the Elimination Method. \[ \begin{aligned} &2 x+3 y=-1 \\ &7 x-6 y=13 \end{aligned} \]
1 answer 168 views
close

Q&A | Subjects | Request Private Tutor | eBook | Wired-up


Join the MathsGee Homework Help & Exam Prep Club where you get study support for success from our community. LEARN - CONNECT - EARN


On the MathsGee Homework Help & Exam Prep Club, you can:


1. Ask questions


2. Answer questions


3. Comment on Answers


4. Vote on Questions and Answers


5. Tip your favourite community member(s)


6. Create/Take Live Video Lessons



Posting on the MathsGee Homework Help & Exam Prep Club


1. Remember the human


2. Behave like you would in real life


3. Look for the original source of content


4. Search for duplicates before posting


5. Read the community's rules




Q&A RULES


1. Answers to questions will be posted immediately after moderation


2. Questions will be queued for posting immediately after moderation


3. Depending on how many posts we receive, you could be waiting up to 24 hours for your post to appear. But, please be patient as posts will appear after they pass our moderation.


Q&A | Subjects | Request Private Tutor | eBook


MathsGee Tools

Math Worksheet Generator

Math Algebra Solver

Trigonometry Simulations

Vectors Simulations

Matrix Arithmetic Simulations

Matrix Transformations Simulations

Quadratic Equations Simulations

Probability & Statistics Simulations

PHET Simulations

Visual Statistics

Q&A | Subjects | Request Private Tutor | eBook