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Answer:
(1) [tex](x,y) = (-2,-4)[/tex]
(2) [tex]y = 4x -26[/tex]
(3) [tex]x = 1[/tex]
Step-by-step explanation:
(1):
[tex]2x - y = 0[/tex]
[tex]x + 3y = -14[/tex]
Required: Solve for x and y
Make x the subject in [tex]x + 3y = -14[/tex]
[tex]x = -3y - 14[/tex]
Substitute -3y - 14 for x in the first equation
[tex]2x - y = 0[/tex]
[tex]2(-3y-14) - y = 0[/tex]
Open bracket
[tex]-6y - 28 - y = 0[/tex]
Collect Like Terms
[tex]- y-6y = 28[/tex]
[tex]-7y = 28[/tex]
Divide both sides by -7
[tex]y = -4[/tex]
Substitute -4 for y in [tex]2x - y = 0[/tex]
[tex]2x - (-4) = 0[/tex]
[tex]2x + 4 = 0[/tex]
Collect Like Terms
[tex]2x = -4[/tex]
Divide by 2
[tex]x = -2[/tex]
Hence, the solution is:
[tex](x,y) = (-2,-4)[/tex]
(2):
[tex](x_1,y_1) = (7,2)[/tex] -- points
[tex]m = 4[/tex] --- slope
Required: Determine the line equation
This is calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
This gives:
[tex]y = 4(x - 7) + 2[/tex]
Open bracket
[tex]y = 4x - 28 + 2[/tex]
[tex]y = 4x -26[/tex]
(3)
[tex]4 - 5x + 3 = 4x - 2[/tex]
Required: Solve for x
Collect Like Terms
[tex]- 5x -4x = - 2-3-4[/tex]
[tex]-9x = -9[/tex]
Divide both sides by -9
[tex]x = 1[/tex]