The point (0, 2) is the only solution to the system of linear equations that contains the equations
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No, (2,2) is not solution of y < 4x - 6
Step-by-step explanation:
To solve above linear problem, we use standard method of Back- Substitution.
First of all, A point (2,2) only becomes solution of equation, if it satisfies equation .
Here, the seems to be like a linear equation.
In this Equation, using Back- Substitution method,
Point (2,2) : first digit 2 corresponds to x- coordinate and second digit 2 corresponds to y-coordinate.
By putting value of x and y in equation (1),
Equation becomes,
.... not true mathematically.
Finally, the result came is not true. Therefore, (2,2) is not solution for equation
The first step in graphing a linear inequality is to graph the linear equality. The equation -x + 4y = -8 is equivalent to 4y = x - 8, which is equivalent to . This is the equation for the line in slope-intercept form, so the line will have a slope of 1/4 and a y-intercept of -2 (see the first image). Notice that the line is solid, rather than dotted. This represents that points on the line are included in the solution, because the inequality sign is ≥, which is not a strict equality (< or >).
Next, we need to figure out which side to shade. To do so, simply pick any point (I like to use the point (0,0) because it makes the calculations easy) and see whether it satisfies the inequality. If it does, shade the side with that point, and if not, shade the opposite side of the graph.
Here we see that the point (0,0) does satisfy the inequality, since -(0) + 4(0) is 0, and 0 ≥ -8, so the top half of the graph should be shaded (see the second image).
