Question

Solve by using substitution. Express your answer as an ordered pair.

Answer 1

Greetings.

Solving by substitution, we can substitute either y-term or x-term. For a fast and better way, I recommend you to substituting x-term.

`- x + 3y = 7 \\ x - 4y = - 10`

Because for x-term, we don't have to move the coefficient to another side as the coefficient for x-terms are both - 1 and 1.

What we need to do is that we move everything to another side excluding x-term.

I will be moving the second equation to another side.

`x = - 10 + 4y`

Now our x-term for the seco d equation is - 10+4y.

Substitute x =-10+4y in the first equation.

`- ( - 10 + 4y) + 3y = 7`

We should get like this. Then we distribute the negative sign in the brackets.

`10 - 4y + 3y = 7`

Remember that negative multiplying negative equal positive.

`- y + 10 = 7`

Subtract as we get -y then we move 10 to another side, leaving y as the subject.

`- y = 7 - 10 \\ - y = - 3 \\ y = ( - 3)/( - 1) \\ y = 3`

Also negative dividing negative equal positive as well. We have the y-value but because it is the two equations. We need to find the x-value as well.

Therefore, substituting y-value in any given equations. It is better to substitute y-value in the equation with less coefficient value.

I will be substituting y-value in the first equation.

`- x + 3y = 7`

Substitute y = 3 in the equation.

`- x + 3(3) = 7 \\ - x + 9 = 7 \\ - x = 7 - 9 \\ - x = - 2 \\ x = ( - 2)/( - 1) \\ x = 2`

Answer in coordinate point/ordered pair as we get (2,3)