Simultaneous Equations: Practice Questions

Solve the following system of linear equations for \(x\) and \(y\):
\(x + y = 12\)
\(x - y = 4\)

The sum of two numbers is 25 and their difference is 7. Let the larger number be \(x\) and the smaller number be \(y\). Solve the simultaneous equations to find the value of the product \(xy\).

In the figure, two straight lines represent the equations \(y = 2x - 4\) and \(y = -x + 5\). If these lines intersect at point \(P\), find the coordinates of \(P\).

Find the value of \(y\) in the system of equations:
\(2x + y = 10\)
\(x = 3\)

Determine the coordinates of the point of intersection for the following two lines:
\(3x - 2y = 7\)
\(x + 4y = 7\)

Solve the following system of linear equations using the method of substitution:
\(y = 3x - 1\)
\(2x + 3y = 19\)

Consider the system of linear equations:
(1) \(3x + 2y = 12\)
(2) \(2x - 3y = -5\)
(a) Use the method of elimination to solve for \(x\) and \(y\).
(b) If these two equations represent two straight lines on a Cartesian plane, state the coordinates of the point where they intersect.