Elimination -- bivariate linear equation The following equations are solved by substitution method （1)（X+Y=7, (3X+Y=17. （2）（2X-7Y=-8, (Y-2X=32. Use the substitution method to solve the following problems （2X+5Y=-21， （X+3Y=8。 I can get this done tonight,

Elimination -- bivariate linear equation The following equations are solved by substitution method （1)（X+Y=7, (3X+Y=17. （2）（2X-7Y=-8, (Y-2X=32. Use the substitution method to solve the following problems （2X+5Y=-21， （X+3Y=8。 I can get this done tonight,

X+Y=7
3X+Y=17.
From x + y = 7
Y=7-X
Substitute 3x + y = 17
3X+7-X=17
2X=10
X=5
Y=7-X=2
2X-7Y=-8,
Y-2X=32.
From y-2x = 32
Y=32+2X
Substituting 2x-7y = - 8,
2X-7(32+2X)=-8
2X-224-14X=-8
12X=-216
X=-18
Y=32+2X=-4

Elimination of linear equation with two variables
5x-3y = x + 2Y (important process)
It is rewritten to express y with an equation containing X

5x-3y = x + 2Y. Move y to the left and X to the right is - 5Y = - 4x. Divide both sides by - 5
Y=4X/5

Known curve C: x ^ 2 + y ^ 2-4mx + 2My + 20m-20 = 0
If the curve C is tangent to the Y axis, find the value of M

(x-2m)^2+(y+m)^2=5m^2-20m+20
The curve C is tangent to the Y axis
2m=√(5m^2-20m+20)
m^2-20m+20=0
The solution is m = 10 ± 4 √ 5