Solutions to 2-variable equations - Questions

Answers

1. A. Only \((1, 4) \)

To check whether an ordered pair \((a,b)\) is a solution of an equation, substitute these values into the equation and determine if the resulting equality is true or false.

To check whether \((1,4)\) is a solution of the equation, let's substitute \(x=1\) and \(y=4\) into the equation:

\(\begin{aligned}

&y=7 x-3 \\

&4=7 \cdot 1-3 \\

&4=7-3 \\

&4=4

\end{aligned}\)

Since \(4=4\), we obtained a true statement, so \((1, 4)\) is indeed a solution of the equation.

To check whether \((-1, -4)\) is a solution of the equation, let's substitute \(x=-1\) and \(y=-4\) into the equation:

\(\begin{aligned}

y &=7 x-3 \\

-4 &=7 \cdot(-1)-3 \\

-4 &=-7-3 \\

-4 &=-10

\end{aligned}\)

Since \(-4 \neq-10\), we obtained a false statement, so \((-1, -4)\) is not a solution of the equation.

Only \((1, 4)\) a solution of the equation.


2. B. Only \((-2, 9) \)

To check whether an ordered pair \((a, b) \) is a solution of an equation, substitute these values into the equation and determine if the resulting equality is true or false.

To check whether \( (2, -9\), let's substitute \(x=2\) and \(y=-9\) into the equation:

\(\begin{aligned}

y &=-2 x+5 \\

-9 &=-2 \cdot 2+5 \\

-9 &=-4+5 \\

-9 &=1

\end{aligned}\)

Since \( -9 \neq 1\), we obtained a false statement, so \((2, -9) \) is not a solution of the equation.

To check whether \( (-2, 9)\), let's substitute \(x=-2\) and \(y=9\) into the equation:

\(\begin{aligned}

&y=-2 x+5 \\

&9=-2 \cdot(-2)+5 \\

&9=4+5 \\

&9=9

\end{aligned}\)

Since \(9 = 9\), we obtained a true statement, so \( (-2, 9 )\) is indeed a solution of the equation.

Only \( (-2, 9 )\) is a solution of the equation.


3. B. Only \((5, 4) \)

To check whether an ordered pair \((a,b)\) is a solution of an equation, substitute these values into the equation and determine if the resulting equality is true or false.

To check whether\((4, 5) \) is a solution of the equation, let's substitute \(x=4\) and \(y=5\) into the equation:

\(\begin{aligned}

2 x+4 y &=6 x-y \\

2 \cdot 4+4 \cdot 5 &=6 \cdot 4-5 \\

8+20 &=24-5 \\

28 &=19

\end{aligned}\)

Since \(28 \neq 19\), we obtained a false statement, so \((4, 5)\) is not a solution of the equation.

To check whether\((5, 4) \) is a solution of the equation, let's substitute \(x=5\) and \(y=4\) into the equation:

\(\begin{aligned}

2 x+4 y &=6 x-y \\

2 \cdot 5+4 \cdot 4 &=6 \cdot 5-4 \\

10+16 &=30-4 \\

26 &=26

\end{aligned}\)

Since \(26 = 26\), we obtained a true statement, so \((5, 4)\) is indeed a solution of the equation.

Only \((5, 4)\)is a solution of the equation.


4. D. Neither

To check whether an ordered pair \((a, b\) is a solution of an equation, substitute these values into the equation and determine if the resulting equality is true or false.

To check whether \((3, 2) \) is a solution of the equation, let's substitute \(x= 3\) and \(y = 2\) into the equation:

\(\begin{aligned}

-x-4 y &=-10 \\

-3-4 \cdot 2 &=-10 \\

-3-8 &=-10 \\

-11 &=-10

\end{aligned}\)

Since \( -11 \neq-10\), we obtained a false statement, so \((3, 2) \) is not a solution of the equation.

To check whether \((-3, 3) \) is a solution of the equation, let's substitute \(x= -3\) and \(y = 3\) into the equation:

\( \begin{aligned}

-x-4 y &=-10 \\

-(-3)-4 \cdot 3 &=-10 \\

3-12 &=-10 \\

-9 &=-10

\end{aligned}\)

Since \(-9 \neq-10\), we obtained a false statement, so \((-3, 3) \) is not a solution of the equation.

Neither of the ordered pairs is a solution of the equation.