How do you solve the system of equations 2x+2y=4 and 5y-3x=6?
Let the equations be Equation A and Equation B respectively ie.,2x + 2y = 4 … A5y - 3x = 6 … BNow lets make at least one variable of the both equations equal, so for that, lets multiply Equation A by 2 and Equation B by 3 and lets them as Equation C and Equation D:(3) * ( 2x + 2y ) = (3) * (4)6x + 6y = 12 … C(2) * ( 5y - 3x ) = (2) * (6)10y - 6x = 12 … DNow let us solve the new equations by adding them:6x + 6y + 10y - 6x = 12 + 1216y = 24y = 24 / 16y = 3 / 2Now let put this value of “y” in ANY of the above equations formed ie., Equation A ,Equation B, Equation C, Equation D. But I am putting it in Equation A:2x + 2y = 42x + (2) * ( 3 / 2 ) = 42x + 3 = 42x = 4 - 32x = 1x = 1 / 2So, the values of “x” and “y” which satisfy the both equations are as under:x = 1 / 2 , y = 3 / 2
How do you solve this system of equations (3x + 5y = 6; 2x - 3y = 4)?
If 3x + 5y = 6, then, multiplying by 2, 6x + 10y = 12. (1) Similarly,if 2x - 3y = 4, then, multiplying by 3, 6x - 9y = 12. (2) Subtract (2) from (1) to get(6x + 10y) - (6x - 9y) = 12 - 12 = 0 => 19y = 0 => y = 0. Substitute this into (1) or (2) toget 3x = 6 or 2x = 4, so x = 2. A quick check shows 3x + 5y = 3*2 + 5*0 = 6 - 0 = 6 and2x - 3y = 2*2 - 3*0 = 4 - 0 = 4, as needed. So (x,y) = (2,0) and you should be able tosolve any pair if linear equations by using this technique. Good Luck!
What is the value of k for which the system of equations Kx+2y=5 and 3x+y=1 has no solution? Later after solving plz tell me what is no solution?
For no solution :Mathematically the equations Written are two linear (straight lines) equations and a solution means A point where these two intersects point is ( values of x,values of y)Since for no solution logically Both the lines should have same slopes i.e. slope Of first line should be equal To slope of the second line Therefore ;Slope of first line = -k/2 = m1Slope of second line = -3 = m2NowPut m1=m2That means K/2 =3 now k =6For k=6 there is no solution.For solution any value Of k except 6 will give the solution.
System of equations & inequalities! pleasee help?
Standard form: 6x+2y=4; 9x+3y=6; substitute/eliminate x = -0.3333y+0.6667 dependent system - infinitely many solutions. x=-0.3333333333333333y+0.6666666666666... Standard form: -4x+2y=2; -2x+y=-3; substitute/eliminate x = +0.5y-0.5 inconsistent system - no solutions. Standard form: 2x-y=7; 3x+2y=14; substitute/eliminate x = +0.5y+3.5 substitute/eliminate y = +1 Solution: x = 4; y = 1; or (x, y) = (4, 1) Standard form: 5x+6y=5; 5x+5y=10; substitute/eliminate x = -1.2y+1 substitute/eliminate y = -5 Solution: x = 7; y = -5; or (x, y) = (7, -5) Standard form: x-2y=7; 3x+4y=6; substitute/eliminate x = +2y+7 substitute/eliminate y = -1.5 Solution: x = 4; y = -1.5; or (x, y) = (4, -1.5) Standard form: -x+y=-3; 2x+y=18; substitute/eliminate x = +1y+3 substitute/eliminate y = +4 Solution: x = 7; y = 4; or (x, y) = (7, 4) Standard form: 5x+2y=4; 2x-2y=10; substitute/eliminate x = -0.4y+0.8 substitute/eliminate y = -3 Solution: x = 2; y = -3; or (x, y) = (2, -3) Standard form: -x-3y=1; x-3y=-1; substitute/eliminate x = -3y-1 substitute/eliminate y = -0 Solution: x = -1; y = 0; or (x, y) = (-1, 0) Standard form: x-2y=-6; 2x-4y=-12; substitute/eliminate x = +2y-6 dependent system - infinitely many solutions. x=+2y-6; Standard form: x-2y=-1; 2x-4y=0; substitute/eliminate x = +2y-1 inconsistent system - no solutions. Standard form: 2x+10y=1; x-4y=-4; substitute/eliminate x = -5y+0.5 substitute/eliminate y = +0.5 Solution: x = -2; y = 0.5; or (x, y) = (-2, 0.5) Standard form: -3x+y=4; 2x+3y=1; substitute/eliminate x = +0.3333y-1.3333 substitute/eliminate y = +1 Solution: x = -1; y = 1; or (x, y) = (-1, 1) Standard form: 3x+4y=7; 4x-2y=24; substitute/eliminate x = -1.3333y+2.3333 substitute/eliminate y = -2 Solution: x = 5; y = -2; or (x, y) = (5, -2) Standard form: x-2y=-1; 2x-3y=4; substitute/eliminate x = +2y-1 substitute/eliminate y = +6 Solution: x = 11; y = 6; or (x, y) = (11, 6)
Solve the system. x – y = 2,3x – 3y = 6?
in the system x-y=2 and 3x - 3y =6, they are the same line Just divide 3x-3y = 6 by three on both sides and it will come out as x - y = 2 parallel lines always have the same slope so the second equation is y = 5/2x +(some number) in this situation y=1 and x = 2, so just plug in those numbers and make both sides of the equation equal each other. y = 5/2(x) +number 1 = 5/2(2) + number 1 = 5 + number 5 plus negative four makes one so... 1 = 5 + (-4) 1 = 1 so the equation is y = 5/2x - 4 third multuply one equation so the the x factors or y factors cancel, here i will multiply the top equation by negative one and then add them (5x – 3y)(-1) = (13)(-1) 4x – 3y = 11 equals -5x + 3y = -13 4x - 3y = 11 + ------------------------- -x = -2 x = 2 now plug in x to get y 4(2) - 3y = 11 8 - 3y = 11 -3y = 3 y = -1 the answer is (2, -1)