Question

Solve the simultaneous equations y =x+2 and x + y = 3

Answer 1

x = 1/2

y = 5/2

Explanation:

So we're gonna use the elimination method, by eliminating one of x or y to find the value of the other one.

y = x + 2 --------------(1)

x + y = 3 --------------(2)

In (1), x is in LHS and y is in RHS. To make things simpler, we take both x and y to the same side.

y = x + 2

y - x = x + 2 - x ( take x to the other side)

y - x = 2-------------------------(3)

Note that in (2), x is positive and in (3), x is negative. So by adding these two, we can single out y because +x and -x cancels out. So we can eliminate x.

(3) + (1) : (x+y) + (y- x) = 3 + 2

2y = 5

y = 5/2

Substituting y = 5/2 for (1),

5/2 - x = 2

5/2 = 2 + x

5/2 - 4/2 = x

x = 1/2

∴ x = 1/2

y = 5/2

Hope i helped you :)

Answer 2

Answer:
`\bold{\bigg((1)/(2),2(1)/(2)\bigg)}\qquad \implies \qquad \bold{\bigg((1)/(2),(5)/(2)\bigg)}`

Explanation:

y = x + 2 x + y = 3

Solve using Substitution Method by replacing y with x + 2:

x + (x + 2) = 3

2x + 2 = 3

2x = 1

x =
`(1)/(2)`

Next, replace x with 1/2 in one of the original equations and solve for y:

y = x + 2

=
`(1)/(2)` + 2

=
`2(1)/(2)`