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.
[tex] - x + 3y = 7 \\ x - 4y = - 10[/tex]
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.
[tex]x = - 10 + 4y[/tex]
Now our x-term for the seco d equation is - 10+4y.
Substitute x =-10+4y in the first equation.
[tex] - ( - 10 + 4y) + 3y = 7[/tex]
We should get like this. Then we distribute the negative sign in the brackets.
[tex]10 - 4y + 3y = 7[/tex]
Remember that negative multiplying negative equal positive.
[tex] - y + 10 = 7[/tex]
Subtract as we get -y then we move 10 to another side, leaving y as the subject.
[tex] - y = 7 - 10 \\ - y = - 3 \\ y = \frac{ - 3}{ - 1} \\ y = 3[/tex]
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.
[tex] - x + 3y = 7[/tex]
Substitute y = 3 in the equation.
[tex] - x + 3(3) = 7 \\ - x + 9 = 7 \\ - x = 7 - 9 \\ - x = - 2 \\ x = \frac{ - 2}{ - 1} \\ x = 2[/tex]
Answer in coordinate point/ordered pair as we get (2,3)
