Open Question
Exercises 86–88 will help you prepare for the material covered in the first section of the next chapter.a. Does (4, −1) satisfy x + 2y = 2?b. Does (4, -1) satisfy x- 2y= 6?
7. Systems of Equations & Matrices
Two Variable Systems of Linear Equations
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Use the elimination method to solve the following system of linear equations.
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Verified step by step guidance1
Start by writing down the system of equations: \(2x + y = 1\) and \(3x - y = 4\).
To use the elimination method, add the two equations together to eliminate \(y\). This means adding \(2x + y = 1\) and \(3x - y = 4\).
When you add the equations, the \(y\) terms cancel out, resulting in \(5x = 5\).
Solve for \(x\) by dividing both sides of the equation \(5x = 5\) by 5, which gives \(x = 1\).
Substitute \(x = 1\) back into one of the original equations, for example \(2x + y = 1\), to find \(y\). This gives \(2(1) + y = 1\), which simplifies to \(y = -1\).
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