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Solve each system in Exercises $1-4$ by using elementary row operations on the equations or on the augmented matrix. Follow the systematic elimination procedure described in this section.$$\begin{array}{rr}{x_{1}+5 x_{2}=} & {7} \\ {-2 x_{1}-7 x_{2}=} & {-5}\end{array}$$

$\left(x_{1}, x_{2}\right)=(-8,3)$

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 1

Systems of Linear Equations

Introduction to Matrices

Chanda G.

September 7, 2021

Can you explain clearly at At 0:27, regarding row 1 and row 2 like step by step. I understand that we are trying to reduce the row below

Jiya G.

February 6, 2022

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So for this problem, we're solving a system of equations, and we're going to do this using row operations in Matrix. So we're going to start by writing the problem as Matrix. And we're going to do that just by copying all of the coefficients into this matrix, which will give us one by seven in the top row and minus two minus seven minus five in the bottom row. So now we can start doing our operations, and the first thing that we're going to do is use this one in the top right corner to cancel out the negative to underneath it. And we'll do that by doing routine equals ro two plus two Road one. And when we do that, we will now have a zero there and a three and a nine after doing those operations to the other entries of the second row. So now we're going to scale this row Ah, by 1/3 in order to get a one in this second column here, and so will he wrote out two times 1/3 which will give us one and three in those positions. So finally, we're going to use this bottom one to kill the five on top of it. And when we do that, we'll get a zero in the top row. Which means that the left hand side of our matrix is now the identity matrix 1001 And that means that this minus 83 is our answers. So that means that we can use this to show that X one is negative eight and X two is three. So what that means is, basically, if we have these two lines, the point where they intersect would be minus eight and three.

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