Answer:
2. -3, 1.
3. -2, 0.
4. 6, 8.
5. 20.
Explanation:
2. x - 3y + 6 = 0
-3y = -x -6
y = 1/3x + 2
y + 4 = -5/4(x - 1)
y + 4 = -5/4x + 5/4
y = -5/4x + 5/4 - 16/4
y = -5/4x - 11/4
If you sketch these two lines on paper (or draw them on a graphing calculator), you will find that they intersect at (-3, 1).
So, the values you enter on the response would be -3, 1.
3. x + 3y = -2
x = -3y - 2
-3x + 5y = 6
-3(-3y - 2) + 5y = 6
9y + 6 + 5y = 6
14y + 6 = 6
14y = 0
y = 0
x + 3 * 0 = -2
x + 0 = -2
x = -2
-3 * -2 + 5 * 0 = 6
Since everything works out, the solution to the two equations is (-2, 0).
So, the values you enter on the response would be -2, 0.
4. 3x - 4y = -14
2x + 5y = 52
2(3x - 4y = -14)
3(2x + 5y = 52)
6x - 8y = -28
6x + 15y = 156
6x + 15y = 156
-6x + 8y = 28
23y = 184
y = 8
3x - 4 * 8 = -14
3x - 32 = -14
3x = 18
x = 6
2 * 6 + 5 * 8 = 12 + 40 = 52
Everything works out, so your solution is (6, 8).
Your answer will be (6, 8).
5. For a system of equations to have no solution, the y's and the x's must have the same coefficients.
5x - Ky - 10 = 0
y = 1/4x + 6
-Ky = -5x + 10
Ky = 5x - 10
1/5Ky = x - 2
1/20Ky = 1/4x - 1/2
1/20K = 1
K = 20
y = 1/4x - 1/2
y = 1/4x + 6
1/4x - 1/2 = 1/4x + 6
1/4x - 1/4x = 6 + 1/2
0 = 6.5
There is no solution, so K = 20.
Hope this helps!!