Question

select the correct answer from each drop-down menu.
a system of linear equations is given by the tables.

x	y		x	y
0	3		0	-1
1	5		2	5
2	7		4	11

the first equation of this system is y = \\(\boldsymbol{\square}\\) x + 3.
the second equation of this system is y = 3x − \\(\boldsymbol{\square}\\).
the solution of the system is ( \\(\boldsymbol{\square}\\) , \\(\boldsymbol{\square}\\) ).

Explanation:

Step1: Find slope of first line

Use two points from first table, e.g., \((0, 3)\) and \((1, 5)\). Slope \(m=\frac{5 - 3}{1 - 0}=2\). So first equation is \(y = 2x + 3\).

Step2: Find constant for second line

Use point \((0, -1)\) in \(y = 3x - c\). Substitute \(x = 0\), \(y=-1\): \(-1=3(0)-c\Rightarrow c = 1\). So second equation is \(y = 3x - 1\).

Step3: Solve system of equations

Set \(2x + 3=3x - 1\). Subtract \(2x\) and add \(1\): \(4=x\). Substitute \(x = 4\) into \(y = 2x + 3\): \(y=2(4)+3 = 11\).

Answer:

First drop - down: \(2\)
Second drop - down: \(1\)
Third drop - down: \(4\)
Fourth drop - down: \(11\)
Solution of the system: \((4, 11)\)