Given:
The system of equations:


To find:
The number that can be multiplied by the second equation to eliminate the x-variable when the equations are added together.
Solution:
We have,
...(i)
...(ii)
The coefficient of x in (i) and (ii) are 1 and
respectively.
To eliminate the variable x by adding the equations, we need the coefficients of x as the additive inverse of each other, i.e, a and -a So, a+(-a)=0.
It means, we have to convert
into -1. It is possible if we multiply the equation (ii) by -5.
On multiplying equation (ii) by -5, we get
...(iii)
On adding (i) and (iii), we get

Here, x is eliminated.
Therefore, the number -5 can be multiplied by the second equation to eliminate the x-variable.
Answer:
See explanation
Step-by-step explanation:
Triangles ΔABC and ΔBAD are congruent. So,
- AB ≅ BA;
- AC ≅ BD;
- BC ≅ AD;
- ∠ABC ≅ ∠BAD;
- ∠BCA ≅ ∠ADB;
- ∠CAB ≅ ∠DBA.
Consider triangles AEC and BED. In these triangles,
- AC ≅ BD;
- ∠EAC ≅ ∠EBD (because ∠CBA ≅ ∠BAD);
- ∠AEC ≅ ∠BED (as vertical angles).
So, ΔAEC ≅ ΔBED. Thus,
AE ≅ EB.
This means that segment CD bisects segment AD.
Hello from MrBillDoesMath!
Answer: (1/7) * ( 4 +\- sqrt(5) i)
where i = sqrt(-1)
Discussion:
The solutions of the quadratic equation ax^2 + bx + c = 0 are given by
x = ( -b +\- sqrt(b^2 - 4ac) )/2a.
The equation 7 x^2 + 3 = 8x can be rewritten as
7x^2 - 8x + 3 = 0.
Using a = 7, b = -8 and c = 3 in the quadratic formula gives:
x = (8 +\- sqrt ( (-8)^2 - 4*7*3) ) / (2*7)
= ( 8 +\- sqrt( 64 - 84)) /(2*7)
= ( 8 +\- sqrt( -20) ) / (2*7)
= ( 8 +\- sqrt( -20) ) / 14
= 8/14 +\- sqrt(5 *4 * -1) /14
= 4/7 +\- 2 sqrt(5) *i /14
As 2/14 = 1/7 in the second term
= 4/7 +\- sqrt(5) *i /7
Factor 1/7 from each term.
= (1/7) * ( 4 +\- sqrt(5) i)
Thank you,
MrB