solve the system of linear equqtions by method of substitution
x + y =3 and x = 1/2y
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- Because we know that x = 1/2y, we can change (a.k.a. substitute) the x to 1/2y in the first equation (x+y=3). [This is called subsitution.] We rewrite this as 1/2y + y = 3.
- Combining like terms, we get 3/2y=3. [We get this because we can rewrite the coefficient for y as 1y or 2/2y and 2/2 + 1/2 = 3/2.] We do this because we want to get the variable by itself.
- To solve means to get the variable by itself. So, we'll need to divide both sides by 3/2. 3/2 ÷ 3/2 = 1, and 3 ÷ 3/2 = 2 [ 3/(3/2) = (3/1)*(2/3) = 2/1 ] We are left with y = 2.
- We are not done yet!Our answer is a coordinate or point with both x and y. If y = 2, what is x? We can substitute our value for y (we got 2) into either equation (we'll get the same value for x for either one because the point is where the two lines intersect). I'll choose the second equation because it's all ready to go and we won't need to move anything around. Substituting in 2 for y in the second equation we get x =1/2(2) = 1.
Our answer is the point (1, 2).
x = 1/2 y = y/2; y/2+y = 3; 1.5y = 3; y = 2
x + 2 = 3; x = 3-2 = 1
x+y = 3 or x = 3-y; (3-y) = 1/2 y = y/2; 3 = y/2 + y = 1.5y; y = 2
x+2 = 3; x = 1