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The solutions of the system of bivariate linear equations of X and y, 3x + 7Y = k, 2x + 3Y = 2, are all positive numbers. Can you find the value of integer k? In the second semester of the second grade of junior high school,
3x+7y=k
2x+3y=2
have to
6x+14y=2k
6x+9y=6
The solution
x=(14-3k)>0 k0 k>3
So k = 4
It is known that M is an integer and - 60 < m ＜ - 30, with respect to the system of bivariate linear equations of X, y 2x−3y＝−5 If − 3x − 7Y = m has an integer solution, find the value of x2 + y
2x-3y = - 5 ① and - 3x-7y = m ②, there are integer solutions to eliminate ① × 3 + ② × 2 to get - 23y = - 15 + 2m, ? m is an integer and - 60 < m ﹤ 30, ? 135 ﹤ 15 + 2m ﹤ 75, that is - 135 ﹤ 23y ﹤ 7513523 ﹥ y ? and ∵ the equation system has integer solution, ? y = 4 or 5 is replaced by 2x-3y = - 5, when y = 4, x = 72
It is known that M is an integer and - 60
X = 4 + 1.5y
m=-3(4+1.5Y)-7Y=-12-11.5Y,
∴-60<-12-11.5Y<-30,
36 / 23 ∵ y is an integer,
Given 3x + 2Y = 0, find the value of the algebraic formula x ^ 2 + xy-y ^ 2 / x ^ 2-xy + y ^ 2
If 3x + 2Y = 0, then x = - 2 / 3 y
（x^2+xy-y^2）/（x^2-xy+y^2）
=（4/9 y²-2/3y²-y²）/（4/9 y²+2/3y²+y²）
=（-11/9 y²）/（19/9y²）
= -11/19
If the system of equations {x + 2Y = 9,3x-y = - 1, then the value of the second power of X and the second power of y-xy is_ (process)
x+2y=9
x=9-2y
Put in 3x-y = - 1
27-6y-y=-1
7y=28
Y=4
x=9-2y=1
So the original formula = 4-16 = - 12
If equations 4x+3y＝5 If the value of X in the solution of KX − (K − 1) y = 8 is 1 greater than that of Y, then K is () A. 3 B. -3 C. 2 D. -2
From the meaning of the title,
The solution is x = 5K + 19
7k−4，y=5k−32
7k−4，
∵ the value of X is one more than the opposite of the value of Y,
ν x + y = 1, namely 5K + 19
7k−4+5k−32
7k−4=1
K = 3,
Therefore, a
If x is equal to y in the solution of {4x + 3Y = 1, ax + (A-1) y = 3, then the value of a is
If x is equal to y in the solution of {4x + 3Y = 1, ax + (A-1) y = 3, then the value of a is
4x+3y=1 (1)
ax+(a-1)y=3 (2)
Because x = y (3)
Substituting (3) into (1) gives: x = 1 / 7 (4), so y = 1 / 7 (5)
Substituting (4) and (5) into (2) gives a = 11
If the solution of the system of bivariate linear equations of X and Y 2x-y = m 3x + y = m + 1 is also the solution of equation 2x + y = 3, find the value of M
The solution of 2x-y=m 3x+y=m+1 is also equation 2x+y=3
Y = 2x-m, substituting 3x + y = m + 1, that is 3x + 2x-m = m + 1 x = (2m + 1) / 5
Substituting x = (2m + 1) / 5 into y = 2x-m, y = (4m + 2) / 5 - M is y = (2-m) / 5
Substitute y = (2-m) / 5, x = (2m + 1) / 5 into 2x + y = 3
（4m+2）/5 +（2-m）/5=3
M = 11 / 3
It is known that the solutions of the binary system of first order equations x-4y = 10 X-my = 5 and 3x + y = 4N, 2x + my = 1 are the same. Try to find the values of M and n
Because the solutions of X and y are the same, the four equations can form an equation group. Change X and Y into the formula expressed by N and m, and replace it with the gradual elimination. You can try it yourself
It is known that the solutions of the system of bivariate linear equations {x-4y = 10 X-my = 5 2x + my = 1 and {3x + y = 4N, 2x + my = 1) are the same. Try to find the values of M and n
From 1: x = 4Y: 4y-my = 5; 8y + my = 1, we get 12Y = 6, so: y = 1 / 2; X = 2; m = - 6
You can bring it into formula 2
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