Is 7 asolution for the equation 2x + 12=3x +(-2x + 5)
1 answer:
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Part A:
x + y = 9
4x + y = 6
To solve this system using substitution, begin by isolating either x or y in the first equation. I'll isolate x.
x + y = 9
x = 9 - y
Substitute this expression (9 - y) into the second equation for x and solve.
4x + y = 6
4(9 - y) + y = 6
36 - 4y + y = 6
36 - 3y = 6
-3y = -30
y = 10
To find x, substitute 10 for y into either of the original equations.
x + y = 9
x + 10 = 9
x = -1
Finally, check all work by substituting the x- and y-values into each original equation.
x + y = 9 --> -1 + 10 = 9 --> 9 = 9 --> True
4x + y = 6 --> 4(-1) + 10 = 6 --> -4 + 10 = 6 --> 6 = 6 --> True
The answer for Part A is x = -1 and y = 10; (-1, 10).
Part B:
For graphing, it's easier to get the equations into slope-intercept form. Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. To get our equations into slope-intercept form, we must simply isolate y.
x + y = 9
y = 9 - x
y = -x + 9
4x + y = 6
y = 6 - 4x
y = -4x + 6
Now that we have our slope-intercept equations, we can easily graph them, since their slopes and y-intercepts are readily visible.
Let's start with the y-intercepts. They are (0, 9) and (0, 6). You can plot those points on the graph.
Now, the slopes. The slope of the first line is -1, this means it declines. To plot this, start where you plotted the y-intercept, count one unit down, and then one unit to the right, and plot that point. Continue doing that and connect the dots, and you will have plotted the first line. The slope of the second line is -4, so it also declines. For this line, count four units down, and then one to the right and plot that point. Likewise, continue this and connect the coordinates, and you will have your line. (See attachment for graph.)
The lines do indeed intersect at (-1, 10); our answer is verified by graphing.
Answer: OPTION A.
Step-by-step explanation:
By definition, a dilation can be an enlargement or a reduction of the shape.
An enlargement is when dilation creates a larger image and a reduction is when dilation creates a smaller image.
When, the scale factor is greater than 1, the image is an enlargement and when the scale factor is between 0 and 1, the image is a reduction.
It is important to know that with a negative scale factor the enlargement will will be inverted and it will also be on the other side of the center of dilation.
Knowing this, we can say that the scale factor that will result in an enlargement is: