Textbook Question
Solve each problem. Find the equation of the line passing through the points of intersection of the graphs of x^2 + y^2 = 20 and x^2 - y = 0.
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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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