1)Find x in the solution of the system 3x+y=2 and 2x-3y=16
A)2
B)-4
C)18/11
D)10/11
I chose A
3x+y=2 times 3 = 9x+3y=6
2x-3y=16 times 1 = 2x-3y=16
11x/11 = 22/11x = 2
2)Find the coordinates of the vertices of the figures formed by y -< x + 2, x + 2 -< 6, and y >- -2
A)(0,0),(2,4),(8,-2)
B)(-4,-2),(2,4),(8,-2)
C)(-4,-2),(4,2),(8,-2)
D)(-2,-4),(2,4),(8,-2)
I chose B
this one confused me this is all the work to show:
-2 -< -4 + 2
2 + 4 -< 6
-2
ok im stuck after this:
y = x + 2
x + y = 6
y = -2
Your inequations form the boundaries of the figure.
So change the < or > to an equal sign, then solve them in pairs.
You should get 3 sets of intersection points.
Solve the pairs of equations just like you did #1.
I will do number one only.
We have this:
(1)Find x in the solution of the system 3x + y = 2 and 2x -3y = 16.
(A)2
(B)-4
(C)18/11
(D)10/11
Your choice = (A)
We have a system of linear equations in two variables.
Here are the two equations:
3x + y = 2...Equations A
2x -3y = 16...Equation B
I will first isolate y in Equation A.
3x + y = 2
y = -3x + 2....I will plug the quantity (-3x + 2) in Equation B to find the value of x.
2x - 3y = 16
2x - 3(-3x + 2) = 16
2x + 9x - 6 = 16
11x - 6 = 16
11x = 16 + 6
11x = 22
x = 22/11
x = 2
Your choice is correct!
Good job!
To find x in the solution of the given system of equations 3x+y=2 and 2x-3y=16, you can use the method of substitution or elimination. Let's use the elimination method to solve this system.
First, we will eliminate one variable by multiplying both sides of the first equation by 2 and both sides of the second equation by 3 to make the coefficients of y equal:
Equation 1: 3x + y = 2 ---> Multiply both sides by 2: 6x + 2y = 4
Equation 2: 2x - 3y = 16 ---> Multiply both sides by 3: 6x - 9y = 48
Now, subtract the second equation from the first equation to eliminate the variable x:
(6x + 2y) - (6x - 9y) = 4 - 48
6x + 2y - 6x + 9y = -44
11y = -44
Divide both sides of the equation by 11 to solve for y:
y = -44/11
y = -4
Now substitute the value of y back into either of the original equations to solve for x. Let's use Equation 1:
3x + y = 2
3x + (-4) = 2
3x - 4 = 2
3x = 6
x = 6/3
x = 2
Therefore, the solution to the system of equations is x = 2 and y = -4. Comparing this with the given options, your choice of answer A) 2 is correct.
For the second problem regarding the coordinates of the vertices of the figures formed by the inequalities y <= x + 2, x + 2 <= 6, and y >= -2, let's analyze each inequality separately.
For the first inequality, y <= x + 2:
To plot this inequality on the coordinate plane, draw a straight line passing through the points (0, 2) and (1, 3) with a solid line. Shade the area below the line because y is less than or equal to (<=) x + 2.
For the second inequality, x + 2 <= 6:
To plot this inequality, draw a vertical line passing through the point (4, 0) with a dashed line. Shade the area to the left of the line because x + 2 is less than or equal to (<=) 6.
For the third inequality, y >= -2:
To plot this inequality, draw a horizontal line passing through the point (0, -2) with a solid line. Shade the area above the line because y is greater than or equal to (>=) -2.
The intersection of the shaded regions, which are the areas satisfying all three inequalities, will give us the vertices of the figure.
Comparing the given answer options, the correct answer is B) (-4, -2), (2, 4), (8, -2).