The fraction 6/11 is equivalent to the fraction of 18/33. They both have the same value. Simply multiply both the numerator and denominator by 3 to the fraction of 6/11 to get the new equivalent one.
I more or less have an understanding, but,
Factor out the GCF of 4x-3 from 5(4x-3)+x(4x-3)
Making it,
(4x-3)(5+x)
We know that the number's opposite is 5. In this context, the opposite means the negative of the given number. Since the number's opposite is 5, the number itself must be -5. This is consistent with the second piece of information, since the absolute value of a number is its distance to 0 and the absolute value of -5 is 5.
From the graph of a quadratic equation, you can find:
The roots. These are the points where the graph crosses the x-axis, and is the solution of the quadratic equation when y=0. Usually, there are either two or zero.
The coefficient of the leading term. In the quadratic equation y= ax^2 + bx + c,
the parabola points upward if a is positive, and downward if a is negative.
The vertex. You can find the vertex, or where the two sides of the parabola meet, by looking at the graph.
The solution to given system of equations is (x, y) = (2, -1)
<em><u>Solution:</u></em>
Given system of equations are:
-1x + 2y = -4 -------- eqn 1
4x + 3y = 5 ------- eqn 2
We can solve the above system of equations by elimination method
<em><u>Multiply eqn 1 by 4</u></em>
4(-1x + 2y = -4)
-4x + 8y = -16 ------ eqn 3
<em><u>Add eqn 2 and eqn 3</u></em>
4x + 3y = 5
-4x + 8y = -16
( + ) --------------------
0x + 11y = -16 + 5
11y = -11
y = -1
<em><u>Substitute y = -1 in eqn 1</u></em>
-1x + 2(-1) = -4
-x -2 = -4
-x = -4 + 2
-x = -2
x = 2
<em><u>Check the answer:</u></em>
Substitute x = 2 and y = -1 in eqn 2
4x + 3y = 5
4(2) + 3(-1) = 5
8 - 3 = 5
5 = 5
Thus the obtained answer is correct
Thus the solution to given system of equations is (x, y) = (2, -1)
