Solve each system by elimination. X+6y=-8 7x+2y=24

Mathematics

2 answers:

m_a_m_a [10]3 years ago

6 0

Answer:

y=-2

x=4

Step-by-step explanation:

equation 1: x + 6y = -8

equation 2: 7x + 2y = 24

To eliminate x first, multiply equation 1 by 7:

7x + 42y = -56

Then subtract the equations from each other:

{ 7x + 42y = -56 } - { 7x + 2y = 24 } = -40y=80

Then we divide both sides by -40 to isolate the <em>y</em>

y = -2

Then we plug -2 into y in one of the equations to find <em>x</em>:

7x+42y=-56

7x+42(-2)=-56

7x-84=-56

7x=28

x=4

adoni [48]3 years ago

3 0

Answer:

8x + 8y = 24

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$2.\\(a-b)^2=a^2-2ab+b^2\\\\x^2-16x=-8\\\\x^2-2(x)(8)=-8\\\\\text{We have}\ 2ab=2(x)(8).\ \text{Therefore}\ b=8.\\\\x^2-2(x)(8)=-8\qquad\text{add}\ 8^2=64\ \text{to both sides}\\\\x^2-2(x)(8)+8^2=-8+64\\\\(x-8)^2=56$

$5.\\2x^2+x-1=2\qquad\text{subtract 2 from both sides}\\\\2x^2+x-3=0\\\\2x^2+3x-2x-3=0\\\\x(2x+3)-1(2x+3)=0\\\\(2x+3)(x-1)=0\iff 2x+3=0\ \vee\ x-1=0\\\\2x+3=0\qquad\text{subtract 3 from both sides}\\2x=-3\qquad\text{divide both sides by 2}\\\boxed{x=-\dfrac{3}{2}}\\\\x-1=0\qquad\text{add 1 to both sides}\\\boxed{x=1}$

$6.\\2x^2-4x=0\qquad\text{divide both sides by 2}\\\\x^2-2x=0\\\\x(x-2)=0\iff x=0\ \vee\ x-2=0\\\\\boxed{x=0}\\\\x-2=0\qquad\text{add 2 to both sides}\\\boxed{x=2}$