Q&A for How to Solve Systems of Equations

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What is the value of two numbers if their sum is 14 and their difference is 2?

Donagan

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x + y = 14. x - y = 2. Add the two equations together: 2x = 16. x =8. 8 - y = 2. y = 6.

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How do I draw the straight line of y = x2 - 7x + 12 and find zeroes of it?

Donagan

Top Answerer

y = x² - 7x + 12 = (x - 3)(x - 4). This is a parabola, not a straight line. To find the zeroes, set (x - 3)(x - 4) equal to zero. That means either (x - 3) or (x - 4) must equal zero. If (x - 3) equals zero, x has to equal 3. If (x - 4) equals zero, x has to equal 4. So the zeroes are 3 and 4.

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How do you do 2x+y=10, 3x-4y=47?

Community Answer

Use the elimination method. First multiply the first equation by 4: 8x + 4y = 40. Now add this equation to the second equation above. The +4y and the -4y cancel each other to eliminate the y term, leaving 11x = 87. Divide both sides by 11: x = 87/11. Now plug this x value into either original equation: 2(87/11) + y = 10. So 174/11 + y = 10, and y = 10 - 174/11 = 110/11 - 174/11 = -64/11. So x=87/11, and y = -64/11. Unwieldy, but there it is. Check the answer by substituting the x and y values into either of the original equations to see if they work. (They do.)

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If a system of equations has no solution, what does the graph look like?

I_l1ke_gam3s

Community Answer

The lines will be parallel, meaning they will never intersect. That is what "no solution" really means.

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Is linear equations hard?

I_l1ke_gam3s

Community Answer

It can be, but with time and practice, it will be super easy to solve any type of systematic equation question.

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Solve for x in 2x = y - 5.

I_l1ke_gam3s

Community Answer

Because you have two variables in one equation, all you can do is solve for x in terms of y. x = (y - 5) / 2.

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How do you solve the system of equations 2x + 2y = 4 and 3x + 9y = 18?

Community Answer

Use the elimination method (because none of the coefficients is 1, and so elimination is easier than substitution). Multiply the first equation by 3 and the second by -2, yielding 6x + 6y = 12 and -6x - 18y = -36. Add the two new equations together: -12y = -24, so y = 2. Plug that y-value into either of the original equations: 2x + 2(2) = 4. Then 2x + 4 = 4. That means x = 0. Check the answers by plugging the x- and y-values into either original equation to see if the equation works.

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What is x - y if 2(x^3 - y^3) = 600 and x^2 + xy + y^2 = 100?

I_l1ke_gam3s

Community Answer

Divide both sides of the first equation by 2 to get x^3 - y^3 = 300. That difference of cubes factors into (x - y)(x^2 + xy + y^2) = 300. We are given that x^2 + xy + y^2 is equal to 100. So (x - y)(100) = 300. Divide both sides of that equation by 100: x - y = 300/100 = 3.

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