Answer:
(3,-2)
Step-by-step explanation:
Part A:
1) <em>Isolate x in x - y = 5</em>
x = y + 5
2) <em>Substitute that x into 4x+y=10</em>
4(y + 5) + y = 10
4y + 20 + y = 10
5y = 10-20
5y = -10
y = -2
3) Use y to solve for x:
x = -2 + 5
x = 3
Part B:
<em>Verify using results from Part A</em>
3 - (-2) = 5
4(3) + (-2) = 12 - 2 = 10
Part C:
<em>Just graph the equations and see where they intersect, which is exactly (3,-2). We got that in Part A and B</em>
Answer:
The slope of the parallel line to the given line is
The equation of the parallel line to the given line and passes through the given point is y + 4 = (x + 2)
The y-intercept of the parallel line to the given line and passes through the given point is
Step-by-step explanation:
In the given figure
∵ The given line passes through points (2, 6) and (-6, 8)
∴ x1 = 2 and y1 = 6
∴ x2 = -6 and y2 = 8
→ Substitute them in the rule of the slope above to find it
∵ m = =
=
∴ The slope of the given line is
∵ Parallel lines have the same slopes
∴ The slope of the parallel line to the given line is
∵ The parallel line passes through the point (-2, -4)
∴ x1 = -2 and y1 = -4
∵ m =
→ Substitute them in the point-slope form above
∵ y - (-4) = (x - (-2))
∴ y + 4 = (x + 2)
∴ The equation of the parallel line to the given line and passes through
the given point is y + 4 = (x + 2)
∵ m =
→ Substitute it in the slope-intercept form above
∴ y = x + b
→ To find b substitute x by -2 and y by -4 (coordinates the given point)
∵ -4 = (-2) + b
∴ -4 = + b
→ Subtract from both sides
∴ = b
∵ b is the y-intercept
∴ The y-intercept of the parallel line to the given line and passes
through the given point is
