Question

.

Solve the system using substitution.
-3x+y=10
-6x+2y=20



no solutions


(–3, 2)


infinite solutions


(3, 0)

Answer 1

The correct answer is infinite solutions

Explanation:

It is given that,

-3x+y=10 -----(1)

-6x+2y=20 -------(2)

eq (1) x 2 ⇒ -6x+2y=20 ----(3)

from this we get eq(2) and eq(3) are same.

Therefore these two equation have infinite solution.

To find the solution using substitution

-3x+y=10 -----(1)

y = 3x +10

Substitute the value of y in eq(2)

-6x+2y=20 -------(2)

-6x +2(3x +10) = 20

-6x + 6x + 20 = 20

20 = 20

Answer 2

Infinite solutions

Explanation:

Given is a system of equations.

-3x+y=10

-6x+2y=20

Equation I when multiplied by 2, gives as

-6x+2y =20 which is the same as equation 2 given.

This gives the two lines are not intersecting nor parallel. But the two lines are coincident with each other.

Hence each point on the line is solution.

Infinite solutions.

Let us try to solve and verify this

BY substitutition we have y = 3x+10, substitute in II

-6x+2(3x+10) =20

Or -6x+6x+20=20

20=20 Thus for any x, this becomes true.

Hence infinite solutions.