ABC and EBF are a pair of vertical angles; mABC = 3x + 8 and mEBF = 2x + 48. What are mABC and mEBF?

1 answer:

3 0

Vertical angles are angles opposite to each other when two lines cross.
what's interesting is that vertical angles are equal.

Based on this:
angle ABC = angle EBF
3x + 8 = 2x + 48
x = 40

measure angle ABC=measure angle EBF =
3(40)+8 = 128 degrees

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D) $\left \{ {{2x-y=7} \atop {2x+7y=31}} \right.$ .

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We solve each system to find the correct answer.

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$\left \{ {{3x-2y=9} \atop {3x+2y=14}} \right.$

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Since the coefficients of y are -2 and 2, we can add the equations to solve, since -2+2=0 and cancels the y variable:
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Next we divide both sides by 6:
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For B:
$\left \{ {{x-y=-2} \atop {4x-3y=11}} \right.$

For this equation, it will be easier to isolate a variable and use substitution, since the coefficient of both x and y in the first equation is 1:
x-y=-2

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x-y+y=-2+y
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We now substitute this in place of x in the second equation:
4x-3y=11
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4(-2)+4(y)-3y=11
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Combining like terms, we have:
-8+y=11

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For C:
Since the coefficient of x in the second equation is 1, we will use substitution again.

x+2y=-11

To isolate x, subtract 2y from each side:
x+2y-2y=-11-2y
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Using the distributive property, we have:
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Combining like terms:
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Subtract 22 from each side:
22+3y-22=-13-22
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Since the coefficients of x are the same in each equation, we will use elimination. We have 2x in each equation; to eliminate this, we will subtract, since 2x-2x=0:

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