Approximate the solution to the system of equations.
y=-x+3 and y=2x+1
a. how do you know what the solution is between the two rows in the table corresponding to x=0.5 and x=1
table:
x y=-x+3 y=2x+1
-1 4 -1
-0.5 3.5 0
0 3 1
0.5 2.5 2
1 2 3
1.5 1.5 4
2 1 5
b complete the table to show the values of x between 0.5 and 1. i already did this
x y= -x+3 y=2x+1
0.5 2.5 2
0.6 2.4 2.2
0.7 2.3 2.4
0.8 2.2 2.6
0.9 2.1 2.8
1 2 3
c. which tow x values will the solution be between? >
d. identify a reasonable approximation for the solution of this system

a) at x=0.5  y=2  and at x=1  y=2 this similarity in values shows that the solution for x is between 0.5 and 1

c) The x  solution will be between  x=0.0 and x=0.7 .

There is a similarity in values of y at x=0.6, y=2.4 and at x=0.7 , y=2.4

d) For x= (0.6+0.7)/2 = 1.3/2 =0.65

   For y= (2.4+2.3)/2 =4.7/2=2.35

  Approximate solution is (0.65, 2.35)

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation: