We know that
If the scalar product of two vectors<span> is zero, both vectors are </span><span>orthogonal
</span><span>A. (-2,5)
</span>(-2,5)*(1,5)-------> -2*1+5*5=23-----------> <span>are not orthogonal
</span><span>B. (10,-2)
</span>(10,-2)*(1,5)-------> 10*1-2*5=0-----------> are orthogonal
<span>C. (-1,-5)
</span>(-1,-5)*(1,5)-------> -1*1-5*5=-26-----------> are not orthogonal
<span>D. (-5,1)
</span>(-5,1)*(1,5)-------> -5*1+1*5=0-----------> are orthogonal
the answer is
B. (10,-2) and D. (-5,1) are orthogonal to (1,5)
Cross multiply.
5.4x=9*25.8
5.4x=232.2 Divide both sides by 5.4
x=43
Hi there!
In order to use the elimination method, you have to create one variable that has the same coefficient. This is to be able to eliminate one variable and have a one variable equation (which you can then solve).
In your case, we'll have the "x" have the same coefficient by multiplying the top equation by 4 and the bottom equation by 2 :
4( -2x + 3y = -4) → -8x + 12y = -16
2( 4x - 2y = 16) → 8x - 4y = 32
Now that both of your equation have a variable with the same coefficient, you need to choose rather you need to add or subtract the equations in order to get rid of the variable (in this case we want to get rid of the "x").
In your case, you want to add both equation together which will give you :
8y = 16
Now that you only have one variable, all you need to do now is solve the equation for "y" :
8y = 16
Divide each side of the equation by 8
y = 2 → Your answer
There you go! I really hope this helped, if there's anything just let me know! :)
Um I think the first one is non proportional and the 2nd one is proportional y is 5 times x the 5 might be a negative
