2xy + 5x -12y -30
x(2y + 5) - 6( 2y + 5)
(2y+5) (x-6)
<span>y = 2−x and y = 4x + 3
Let I be the point of intersection:
I belongs to the line y=2-x and at the same time I belongs to y=4x+3, then the coordinates of I are the same for y =2-x & y= 4x+2, in short if we replace the coordinates in y = 2-x & in y=4x+3 by their respective values, we will find an equality.
b) <span>2−x = 4x + 3
Replace x in the equation 2−x = 4x + 3 with the here below values to find if an equality exists
for x = -3 then </span> 2-(-3) = 4(-3)+3 → 5 = -9 IMPOSSIBE, it's not an equality
for x = 2 then 2-2 = 4(2)+3 →<span> 0 = 11 IMPOSSIBE, it's not an equality
</span>for x = 1 then 2-(1) = 4(1)+3 →<span> 1 = 7 IMPOSSIBE, it's not an equality
</span>for x = - 1 then 2-(-1) = 4(-1)+3 →<span> 3 = -1 IMPOSSIBE, it's not an equality
and you can replace x with all integers from - 3 to + 3 and you will find an INEQUALITY, so all these values are not a solution of thev equation
c. Solving the equation </span><span>2−x = 4x + 3
</span><span>2−x = 4x + 3
1st add x to both sides: 2-x + x = 4x + 3 + x </span>→2 = 5x + 3
2nd to this new equation <span>2 = 5x + 3, subtract 3 from both sides:
</span><span>2 - 3= 5x + 3 - 3 </span>→-1 = 5x
3rd in this new equation -1=5x, divide both sides by 5 → -1/5 = x
And x = -1/5 is the solution of the system. To find the y value, you replace in any of the 2 equation <span>y = 2−x and y = 4x + 3, x by its value (-1/5) and you will find y = 11/5</span>
</span>
Answer:
(y+2) = (1/3)(x-1)
Answer in point-slope form, you can rearrange this into the form which you need.
Step-by-step explanation:
recall that the general point-slope form of a linear equation looks like :
(y - y₁) = m(x - x₁)
where m is the slope and (x₁,y₁) is any point on the line
here we are given m = 1/3 and (x₁,y₁)=(1,-2)
simply substitute this info into the general equation above
(y - y₁) = m(x - x₁)
(y - (-2) ) = (1/3)(x - 1)
(y+2) = (1/3)(x-1) Answer in point-slope form, you can rearrange this into the form which you need.
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