Solve each system by elimination. In systems with fractions, firs...

Question

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2.
(2x-1)/3 + (y+2)/4 = 4
(x+3)/2 - (x-y)/2 = 3

Accepted Answer

Hello everybody. Everything. All right today that we're going to be looking at this question that states using the elimination method, solve the following system of equations where our equations will have equation one will be three X minus two in the numerator divided by six in the denominator plus Y plus four as a numerator divided by eight in the denominator, that'll be equal to 15. An equation number two will be X plus five in the numerator divided by three in the denominator minus X minus Y in the numerator divided by three in the denominator. And that will also be equal to 15. And the answer choice provided are a axis equals to 38 divided by seven, Y equals 20 B ax is equal to 20 divided by seven, Y equals 38 C equals C is axis equal to 40 divided by three, Y equals 59 D is axis equal to 59 divided by three and Y of 40. No. When they're telling us that we're using the elimination method, that means we have to see what, how we can manipulate each of our equations to once we add them up. If we add up the equations, we will be eliminating one of the variables. So let's try to do that. So in this case, we're going to multiply equation one by 24. So we have 24 multiplying the three X minus two divided by six plus Y plus four divided by eight equals 15. So including the equals 15, we're multiplying the entire equation by 24 an equation two will be multiplied by three. So we have three multiplying the X plus five divided by three minus X minus Y divided by three equals 15 as well. Since we're multiplying the equation or the entire equation including the answer. Now, if we distribute all that, we'll have that equation. One will be four multiplying three X minus two because we're basically just since there's fractions and we're multiplying by the 24 we're basically just doing 24 divided by six. So I have four multiplying the three X minus two, which was the numerator and that'll be plus three because 24 divided by eight is three, multiplying the generator which is Y plus four and that will be equal to 360 which is 15, multiplied by 24. And equation number two will be simply the numerator. So X plus five minus the numerator once again X minus Y and the X minus Y is in a parentheses. So we have that equal to 45. So in equation number two, the minus is actually multiplying the X minus Y. So let's simplify that a bit further. So we have equation one is equal to 12, X minus eight plus three, Y plus 12 equals 316. An equation two will now be X plus five minus X plus Y because we distributed the negative, so it'll be a negative multiplied by a positive X so minus X and a negative multiplied by a negative Y which is plus Y and that'll be equal to 45. Now, for now, let's continue to simplify this. So we have, actually, if we only focus on equation number two, we have X minus X which is zero. And we've eliminated the X variable now, so we have Y plus five equals 45. And now we can go ahead and solve for the Y which is, it will bring up five over from the left hand side to the right hand side. We have that Y equals 40. So that'll be our answer for the Y value. Now, we can continue to simplify equation one. So we'll have 12 X plus three, Y plus four because negative eight plus 12 is positive four, that'll be equal to 316. And now we can plug in the Y for our three Y. So we'll have 12 X plus three multiplied by 40 plus four equals 360. And now we can distribute the three and add the four. So three multiplied by the 40 is 120 plus four is 124. So we have 12 X plus 124 equals 360. And if we subtract the 1 24 from the left, so we move it from the left hand side to the right hand side by subtracting, we have that 12 X is equal to 236. And now we divide both sides by 12. We'll get that X is equal to 236 divided by 12. And that won't be a whole number. So we'll have that X is equal to, if we simplify this by dividing the numerator and the denominator by four, we'll have that X is equal to 59 divided by three. And that'll be our second answer for this question. So that matches with answer choice. Dean X equals 59 divided by three and Y equals 40. So I hope that was helpful. And until next time.

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. (2x-1)/3 + (y+2)/4 = 4 (x+3)/2 - (x-y)/2 = 3

Key Concepts

Systems of Equations

Elimination Method

Clearing Denominators

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