Problem

Solve the system by either the substitution or th…

01:23

Problem 82 Hard Difficulty

Solve the system by either the substitution or the elimination method.
$$
\left\{\begin{array}{l}
{3 x=20 y+1} \\
{0.04 x+0.05 y-0.33=0}
\end{array}\right.
$$

Answer

$x=7$
$y=1$

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Algebra

Elementary and Intermediate Algebra

Chapter 4

Systems of Linear Equations and Inequalities

Section 3

Solving Systems of Equations by Elimination (Addition)

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Video Transcript

Okay, let's do a little simplifying of these equations. The second equation. We can multiply by 100 to clear out the decimals and then both equations. We want to change to standard form if we're going to use elimination. So with the second equation, if I multiply it by 100 I have for X Plus five. Why minus 33 equal zero. So now changing both equations into standard form. In the first equation, I'm going to subtract 20 wife from both sides. So three X minus 20 y equals one. And in the second equation, I'm going to add 33 to both sides. So for X Plus five y equals 33. Now we can use elimination and eliminate Why, If we multiply the second equation by four. So the first equation is staying the same. Three x minus 20 y equals one on the second equation, multiplied by four is 16 x plus 20 y equals 100 better. Double check here. Make sure I don't get it running 33 times for 1 32 Okay, let's add those equations together. The Ex Terms at 2 19 x The white terms are eliminated and the Constance at 2133. Let's see what 1 33 divided by 19 ISS. That gives us seven. So we have X equals seven. Okay, So now to find why we're gonna go back to one of our equations either equation one or equation, too. I think I'll choose Equation one and substitute our way. Our value for X back in there. So in equation One, we have three times x. So three times seven minus 20 times y equals one. So 21 when it's 20 y equals one. If we subtract 21 from both sides, we have negative. 20 y equals negative 20. So divide by negative 20 and you get y equals one. Let's check our answer and make sure that we didn't make any mistakes using equation, too. So an equation to we have four times x. So four times seven plus five times why five times one equals 33. Let's see if that works. For times seven is 28 5 times one is 5 28 plus five is 33. That's a good check. Now we can write our answer as he ordered pair X comma y seven comma one

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