X - Y = 7 eqn 1X + Y = 29 eqn 2Taking eqn 1 we can isolate for XX-Y = 7add Y to both sidesX = 7 + YSubstituting this into eqn 2 we getX + Y = 29(7 + Y) + Y = 297+ 2Y = 29subtract 7 from both sides2Y = 22divide both sides by 2Y = 11Substituting this into eqn 1 we getX - 11 = 7add 11 to both sidesX = 18So X = 18 and Y = 11
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17
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-5
9y-11=7 +11 +11 9y=18 y=2
1) x*y=315 2) x+y=52 from 2, x=52-y, put into 1, y*(52-y) = 315 or y^2-52*y+315=0 delta= (-52)^2-4*1*315=1444 = 38^2 y = (52-38)/2 = 7 or y = (52+38)/2 = 45 then x = 45 or x = 45
11
Where is y in the first equation, you put its equivalent (=) -3x + 11 The first equation is then transformed into: 3x + 2*(-3x + 11) = 7. Then you get: 3x + (-6x) + 2*11 = 7 <=> -3x + 22 = 7 <=> 22 - 7 = 3x <=> 3x = 15 <=> x = 15/3 <=> x = 5. Then you substitute the x in the second equation by its equivalent so, (x = 5) y = -3*x + 11 <=> y = -3*5 + 11 <=> y = -15 + 11 <=> y = -4. x = 5. y = -4.
1
If: y = x^2 -2x -7 and y = 2x +k Then: x^2 -2x -7 = 2x +K Transposing terms: x^2 -4x +(-7 -k) = 0 Using the discriminant formula: 4^2 -4*1*(-7 -k) = 0 => k = -11 Using the quadratic equation formula: x^2 -4x +4 = 0 => x = 2 By substitution: y = -7 Therefore the values of the variables are: k = -11, x = 2 and y = -7
y/7 + 6 = 11 Subract 6 from bot sides: y/7 = 11 - 6 = 5 Multiply both sides by 7: y = 5*7 = 35
1. (1/10)x=(1/9)y --> 2. (1/10)x/(1/9)=y --> 3. (9/10x)=y 4. Plug into other equation.x+y=38 4. x+9/10x=38 ----> 5. 1.9x=38 --> 6. x=20 7. Plug x into one of the original equaitons.7. 20+y=38 --> 8. y=18x=20,y=18
X - Y = 7 eqn 1X + Y = 29 eqn 2Taking eqn 1 we can isolate for XX-Y = 7add Y to both sidesX = 7 + YSubstituting this into eqn 2 we getX + Y = 29(7 + Y) + Y = 297+ 2Y = 29subtract 7 from both sides2Y = 22divide both sides by 2Y = 11Substituting this into eqn 1 we getX - 11 = 7add 11 to both sidesX = 18So X = 18 and Y = 11
It is 2y + 22 = 2(y + 11)
y=11
Points: (7, 0) and (0, 11) Slope: 0-11/7-0 = -11/7 Equation: y-0 = -11/7(x-7) => 7y = -11x+77 Equation: y-11 = -11/7(x-0) => 7y = -11x+77