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kolbaska11 [484]
3 years ago
8

Examine the system of equations. Which is an equivalent form of the first equation that when added to the second equation elimin

ates the y terms? Negative StartFraction 5 Over 8 EndFraction x + three-fourths y = 12 8 x + 12 y = 11
Mathematics
1 answer:
seraphim [82]3 years ago
8 0

Answer:

10x - 12y = 192

Step-by-step explanation:

Given the equation :

-5/8x + 3/4y = 12 - - - (1)

8x + 12y = 11 ___(2)

The equivalent form of the first equation which can eliminate the y term :

Multiply (1) by - 16 :

-5/8x * - 16 + 3/4y * - 16 = 12 * - 16

10x - 12y = 192

Hence, Adding the obtained equation and equation(2) will eliminate.

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\large\boxed{x=\dfrac{9}{8}-\dfrac{\sqrt{109}}{8},\ y=-\dfrac{1}{2}-\dfrac{\sqrt{109}}{18}}\\or\\\boxed{x=\dfrac{9}{8}+\dfrac{\sqrt{109}}{2},\ y=-\dfrac{1}{2}+\dfrac{\sqrt{109}}{18}}

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\left\{\begin{array}{ccc}4x\times9y=7&(1)\\4x-9y=9&(2)\end{array}\right\\\\(2)\\4x-9y=9\qquad\text{subtract}\ 4x\ \text{from both sides}\\-9y=-4x+9\qquad\text{change the signs}\\9y=4x-9\qquad\text{substitute it to (1)}\\\\4x(4x-9)=7\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\(4x)(4x)+(4x)(-9)=7\\(4x)^2-36x=7\\(4x)^2-2(4x)(4.5)=7\qquad\text{add}\ 4.5^2\ \text{to both sides}\\(4x)^2-2(4x)(4.5)+4.5^2=7+4.5^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2

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