To solve:
re-arrange the first to make y the subject and substitute for y in the second:
And solving the second:
1/2 (7 + 3x) = x2 - 2x + 3
→ 7 + 3x = 2x2 - 4x + 6
→ 2x2 - 7x - 1 = 0
→ x = 1/4 (7 ± √57)
And substituting back into the (rearranged) first equation:
y = 1/2 (7 + 3x)
= 1/2 (7 + 3(1/4 (7 ± √57)))
= 1/2 (28/4 + 3/4 (7 ± √57)))
= 1/8 (49 ± 3√57)
giving the two solutions:
Note: the value of y is worked out once for each of the +/- of the √57; in this case +√57 for x leads to +√57 for y, and -√57 for x leads to -√57 for y. I showed the calculation in one for both.
To check the result, a substitution can be made in the original equation 2:
x = 1/4 (7 ± √57):
y = (1/4 (7 ± √57))2 - 2(1/4 (7 ± √57)) + 3
= 1/16 (7 ± √57))2 - 8/16(7 ± √57) + 48/16
= 1/16 (49 ± 14√57 + 57 - 56 - ±8√57 + 48)
= 1/16 (96 ± 6√57) [see below]
= 1/8 (49 ± 3√57) as before
Can't be done unless you have another equation with the same x and y. Then you would solve for simultaneous equations.
4
Simultaneous equations are where you have multiple equations, often coupled with multiple variables. An example would be x+y=2, x-y=2. To solve for x and y, both equations would have to be used simultaneously.
If you already know that x = -3 and y = 5 what linear equations are you wanting to solve?
You cannot solve this equation without some more information. The value of y depends upon the value of x, but they could take infinitely many different values. Maybe this is just one of a pair of simultaneous equations? If so, you need both equations to find values for x and y.
Its called Simultaneous Equations
Can't be done unless you have another equation with the same x and y. Then you would solve for simultaneous equations.
Graphically might be the simplest answer.
solve systems of up to 29 simultaneous equations.
4
Parallel lines never meet and so parallel equations do not have any simultaneous solution.
Solve simultaneous equations of up to 29 variables.
The elimination method only works with simultaneous equations, hence another equation is needed here for it to be solvable.
Simultaneous equations are where you have multiple equations, often coupled with multiple variables. An example would be x+y=2, x-y=2. To solve for x and y, both equations would have to be used simultaneously.
The most common use for inverted matrices is to solve a set of simultaneous equations.
simultaneous equationshttp://www.answers.com/main/Record2?a=NR&url=http%3A%2F%2Fcommons.wikimedia.org%2Fwiki%2FImage%3AEmblem-important.svg: === === : === === === === # # # # # === ===: === === : === === : === === : === === : === ===
This equation is not possible unless you are given another equation related to x and y. Then you could use simultaneous equations to solve this. However in this came this question is impossible