Solving inequalities and graphing:
y<2x+4
-3x-2y greater than or equal to 6
how to solve?
Thanks
Is (3, 2) a solution to this system of equations? 8x + 7y = 37
2y = 4x - 2 (duh...a+ yes
To solve the inequalities and graph them, you need to follow these steps:
1. Solve the first inequality, y < 2x + 4:
To graph this inequality, first, graph the equation y = 2x + 4 as a dotted line. This line represents where y is equal to 2x + 4. Since the inequality is y < 2x + 4, the line should be dotted to indicate "less than." Choose a few test points (not on the line) to determine which side of the line satisfies the inequality. If a test point satisfies the inequality, shade the region on that side of the line. If the test point does not satisfy the inequality, shade the region on the other side of the line.
2. Solve the second inequality, -3x - 2y ≥ 6:
To graph this inequality, first, graph the equation -3x - 2y = 6 as a solid line. This line represents where -3x - 2y is equal to 6. Since the inequality is -3x - 2y ≥ 6, the line should be solid to indicate "greater than or equal to." Choose a few test points (not on the line) to determine which side of the line satisfies the inequality. If a test point satisfies the inequality, shade the region on that side of the line. If the test point does not satisfy the inequality, shade the region on the other side of the line.
3. Graph the solutions:
The shaded regions for both inequalities represent the solutions. The area where the shaded regions overlap is the solution that satisfies both inequalities.
I'm unable to create a visual graph here, but you can try using online graphing tools or software to plot the inequalities and see the solution visually.
To solve the given inequalities and graph them, you can follow these steps:
1. Solve the first inequality, y < 2x + 4:
a. First, rewrite the inequality in the form y = 2x + 4.
b. This equation represents a straight line with a slope of 2 and a y-intercept of 4.
c. Since the inequality is y < 2x + 4, the solution comprises all points below the line but not including the line itself.
d. To graph this inequality, draw a dashed line representing y = 2x + 4, and shade the region below the line.
2. Solve the second inequality, -3x - 2y ≥ 6:
a. Start by rewriting the inequality in the form y = -3/2x - 3.
b. This equation represents a straight line with a slope of -3/2 and a y-intercept of -3.
c. Since the inequality is -3x - 2y ≥ 6, the solution encompasses all points on or below the line.
d. To graph this inequality, draw a solid line representing y = -3/2x - 3, and shade the region below the line.
The shaded regions from both inequalities will overlap, indicating the solution to the system of inequalities.