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ntext Inequality Systems Graphically (Level 1)
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Penalty: 0.5 off
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Henry and his children went into a restaurant that sells drinks for 
$2 each and tacos for 
$4 each. Henry has 
$40 to spend and must buy at least 14 drinks and tacos altogether. If 
x represents the number of drinks purchased and 
y represents the number of tacos purchased, write and solve a system of inequalities graphically andidetermine one possible solution.
Inequality 
1:y >= 
◻ plot 
◻
Inequality 
2:y >= 
◻ plot

ntext Inequality Systems Graphically (Level 11)\newlineScore: 0/10 0 / 10 \newlinePenalty: 00.55 off\newlineQuestion\newlineWatch Video\newlineShow Examples\newlineHenry and his children went into a restaurant that sells drinks for $2 \$ 2 each and tacos for $4 \$ 4 each. Henry has $40 \$ 40 to spend and must buy at least 1414 drinks and tacos altogether. If x x represents the number of drinks purchased and y y represents the number of tacos purchased, write and solve a system of inequalities graphically andidetermine one possible solution.\newlineInequality 1:y 1: y \geq \square plot \square \newlineInequality 2:y 2: y \geq \square plot

Full solution

Q. ntext Inequality Systems Graphically (Level 11)\newlineScore: 0/10 0 / 10 \newlinePenalty: 00.55 off\newlineQuestion\newlineWatch Video\newlineShow Examples\newlineHenry and his children went into a restaurant that sells drinks for $2 \$ 2 each and tacos for $4 \$ 4 each. Henry has $40 \$ 40 to spend and must buy at least 1414 drinks and tacos altogether. If x x represents the number of drinks purchased and y y represents the number of tacos purchased, write and solve a system of inequalities graphically andidetermine one possible solution.\newlineInequality 1:y 1: y \geq \square plot \square \newlineInequality 2:y 2: y \geq \square plot
  1. Write Inequality for Total Amount: Write the inequality for the total amount Henry can spend: 2x+4y402x + 4y \leq 40.
  2. Write Inequality for Minimum Number: Write the inequality for the minimum number of drinks and tacos: x+y14x + y \geq 14.
  3. Graph First Inequality: Graph the first inequality: 2x+4y402x + 4y \leq 40. This is a line with a slope of 12-\frac{1}{2} and y-intercept at (0,10)(0, 10). Shade the area below the line because we're looking for values of xx and yy that make the inequality true.
  4. Graph Second Inequality: Graph the second inequality: x+y14x + y \geq 14. This is a line with a slope of 1-1 and y-intercept at (0,14)(0, 14). Shade the area above the line because we're looking for values of xx and yy that make the inequality true.
  5. Find Intersection: Find the intersection of the two shaded areas. This intersection represents the possible combinations of drinks and tacos Henry can buy.
  6. Choose Point: Choose a point within the intersection area. For example, if Henry buys 1010 drinks (x=10)(x=10), he can spend the remaining $20\$20 on tacos, which means he can buy 55 tacos (y=5)(y=5).

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