Simultaneous Equations- Substitution - Questions

Question 1
49330

Solve simultaneously
\(y=x-3\)
\(2x+3 y=26\)

\(x=7, y=4\)

Question 2
49331

Solve simultaneously
\(y=3x-2\)
\(5 x-2y=5\)

\(x=-1, y=-5\)

Question 3
49332

Solve simultaneously
\(y=2x-12\)
\(y=13-3 x\)

\(x=5, y=-2\)

\begin{align}
&\begin{aligned}
y&=2 x-12 \ldots(1) \\
y&=13-3 x \ldots(2) \\
\end{aligned}\\
&\text {Substitute (1)into (2)} \\
&\begin{aligned}
2x-12&=13-3 x \\
2 x-12+12&=13+12-3 x \\
2 x&=25-3 x \\
5 x&=25 \\
x&=5\\
\\
y&=2x-12\\
&=2(5)-12\\
y&=-2
\end{aligned}
\end{align}

Question 4
49333

Solve simultaneously
\(x=2y-7\)
\(x=13-6y\)

\(x=-2, y=2.5\)

Question 5
49334

Solve simultaneously
\(\begin{aligned}
7x+4y&=-7\\
5x+y&=8
\end{aligned}\)

\(x=3, y=-7\)

Question 6
49335

Solve simultaneously 
\(\begin{aligned}
x-2 y&=2 \\
3x-8 y&=11
\end{aligned}\)

\(x=-3, y=-2.5\)

Question 7
49336

Solve simultaneously
\(\begin{aligned}
3x+2y &=0 \\
6x+7y &=6
\end{aligned}\)

\(x=-\dfrac{4}{3}, y=2\)

Question 8
49337

Solve simultaneously
\(\begin{aligned}
x-4y&=4\\
5x-12y&=18
\end{aligned}\)

\(x=3, y=-\dfrac{1}{4}\)

Question 9
15571

Solve the following simultaneous equations using substitution method

\(x + 15y = 20\)

\(3x - 8y = 7\)

\(x = 5,\,\,\,y = 1\)

Question 10
15572

Solve the following simultaneous equations using substitution method

\(9x -2y = 20\)

\(5x +y = 9\)

\(x = 2,\,\,\,y = - 1\)

Question 11
15573

Solve the following simultaneous equations using substitution method

\(6x - y = 15\)

\(11x + 7y = 1\)

\(x = 2,\,\,\,y = - 3\)

Question 12
15574

Solve the following simultaneous equations using substitution method

\(3x + 17 = 11y\)

\(3y = x + 1\)

\(x = 20,\,\,\,y = 7\)

Question 13
15575

Solve the following simultaneous equations using substitution method

\(5x - 4y = 8\)

\(2x + y = 50{\rm{ }}\)

\(x = 16,\,\,\,y = 18\)