Open Question
Use a system of equations to solve each problem. See Example 8. Find an equation of the parabola y = ax^2 + bx + c that passes through the points (2, 3), (-1, 0), and (-2, 2).
7. Systems of Equations & Matrices
Two Variable Systems of Linear Equations
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Use substitution to solve the following system of linear equations.
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Verified step by step guidance1
Start by identifying the two equations in the system: \(4x + y = 1\) and \(x - y = 4\).
Choose one of the equations to solve for one variable. Let's solve the second equation \(x - y = 4\) for \(x\). Rearrange it to get \(x = y + 4\).
Substitute \(x = y + 4\) into the first equation \(4x + y = 1\). This gives \(4(y + 4) + y = 1\).
Simplify the equation \(4(y + 4) + y = 1\) to find the value of \(y\). Distribute the 4 to get \(4y + 16 + y = 1\), then combine like terms to get \(5y + 16 = 1\).
Solve the equation \(5y + 16 = 1\) for \(y\). Once you find \(y\), substitute it back into \(x = y + 4\) to find \(x\).
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