Question

which statements are true about the ordered pair (2, 3) and the system of equations?
3x + 4y = 18
2x - 2y = 2
select each correct answer.
the ordered pair (2, 3) is a solution to the system of linear equations
when (2, 3) is substituted into the first equation, the equation is true.
when (2, 3) is substituted into the second equation, the equation is true
when (2, 3) is substituted into the second equation, the equation is false
when (2, 3) is substituted into the first equation, the equation is false
the ordered pair (2, 3) is not a solution to the system of linear equations.

Explanation:

Step1: Substitute into first equation

Substitute $x=2$, $y=3$ into $3x+4y=18$:

$$\begin{align*} 3(2)+4(3)&=6+12\\ &=18 \end{align*}$$

Step2: Substitute into second equation

Substitute $x=2$, $y=3$ into $2x-2y=2$:

$$\begin{align*} 2(2)-2(3)&=4-6\\ &=-2 eq2 \end{align*}$$

Step3: Evaluate system solution

A solution to the system must satisfy both equations. Since $(2,3)$ fails the second equation, it is not a system solution.

Answer:

• When (2, 3) is substituted into the first equation, the equation is true.
• When (2, 3) is substituted into the second equation, the equation is false.
• The ordered pair (2, 3) is not a solution to the system of linear equations.