<em>kx</em> + <em>z</em> = 3 means <em>z</em> = 3 - <em>kx</em>. Substitute this into the first two equations:
<em>x</em> + <em>y</em> + 3 (3 - <em>kx</em>) = 10 ==> (1 - 3<em>k</em>) <em>x</em> + <em>y</em> = 1
-4<em>x</em> + 3<em>y</em> + 5 (3 - <em>kx</em>) = 7 ==> (-4 - 5<em>k</em>) <em>x</em> + 3<em>y</em> = -8
Multiply through the first equation by -3 :
-3 ((1 - 3<em>k</em>) <em>x</em> + <em>y</em>) = -3 (1) ==> (-3 + 9<em>k</em>) <em>x</em> - 3<em>y</em> = -3
Add this to the second equation to eliminate <em>y</em> :
((-3 + 9<em>k</em>) <em>x</em> - 3<em>y</em>) + ((-4 - 5<em>k</em>) <em>x</em> + 3<em>y</em>) = -3 + (-8)
(-7 + 4<em>k</em>) <em>x</em> = -11
Normally, you would solve for <em>x</em> by dividing both sides by -7 + 4<em>k</em>. But you can't do that if this turns out to be equal to 0, which happens for
-7 + 4<em>k</em> = 0 ==> <em>k</em> = 7/4
Answer:
1.
Step-by-step explanation:
We are trying to find out what is equal to 2(10x+4y)
2(10x+4y)
because 2 times 10x is 20x, 4y times 2 is 8y!
