Linear Equations in Two Variables

1. Which ordered pair is a solution of the equation?

$y=7 x-3$

Choose 1 answer:

A. Only $(1, 4)$

B. Only $(-1, -4)$

C. Both $(1, 4)$ and $(-1, -4)$

D. Neither

2. Which ordered pair is a solution of the equation?

$y=-2 x+5$

A. Only $(2, -9)$

B. Only $(-2, 9)$

C. Both $(2, -9)$ and $(-2, 9)$

D. Neither

3. Which ordered pair is a solution of the equation?

$2 x+4 y=6 x-y$

A. Only $(4, 5)$

B. Only $(5, 4)$

C. Both $(4, 5)$ and $(5, 4)$

D. Neither

4. Which ordered pair is a solution of the equation?

$-x-4 y=-10$

A. Only $(3, 2)$

B. Only $(-3, 3)$

C. Both $(3, 2)$ and $(-3, 3)$

D. Neither

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.

1. $y-4=-2(x+3)$

Complete the missing value in the solution to the equation.

$(-3, \text { ____ })$

2.$-4 x-y=24$

Complete the missing value in the solution to the equation.

$(\text { ____ }, 8)$

3. $-3 x+7 y=5 x+2 y$

Complete the missing value in the solution to the equation.

$(-5, \text { ____ })$

4. $2 x+3 y=12$

Complete the missing value in the solution to the equation.

$(\text { ____ }, 8)$

1. $(-3,4)$

To find the $y$-value that corresponds to $x=3$, let's substitute this $x$-value in the equation.

$\begin{aligned} &y-4=-2(x+3) \\ &y-4=-2(-3+3) \\ &y-4=-2 \cdot 0 \\ &y-4=0 \\ &y=4 \end{aligned}$

Therefore $(-3,4)$ is a solution of the equation.

2. $(-8, 8)$

To find the $x$-value that corresponds to $y=8$, let's substitute this $y$-value in the equation.

$\begin{aligned} -4 x-y &=24 \\ -4 x-8 &=24 \\ -32 &=4 x \\ -8 &=x \end{aligned}$

Therefore $(-8, 8)$ is a solution of the equation.

3. $(-5, -8)$

To find the $y$-value that corresponds to $x = -5$, let's substitute this xxx-value in the equation.

$\begin{aligned} -3 x+7 y &=5 x+2 y \\ -3 \cdot(-5)+7 y &=5 \cdot(-5)+2 y \\ 15+7 y &=-25+2 y \\ 5 y &=-40 \\ y &=-8 \end{aligned}$

Therefore $(-5, -8)$ is a solution of the equation.

4. $(-6, 8)$

To find the $x$-value that corresponds to $y = 8$, let's substitute this yyy-value in the equation.

$\begin{aligned} 2 x+3 y &=12 \\ 2 x+3 \cdot 8 &=12 \\ 2 x+24 &=12 \\ 2 x &=-12 \\ x &=-6 \end{aligned}$

Therefore $(-6, 8)$ is a solution of the equation.