In this section we * learn how to solve simultaneous equations involving quadratics and linears*.

For example, by the end of this section we'll know how to solve either of the following pair of *simultaneous equations*:

In this first section we learn *how to solve simultaneous equations* such as:
\[\begin{aligned} & y = x^2 + 5x - 7 \\ & y = 2x + 3 \end{aligned}\]
The method used is the ** method of substitution**.

When solving such simultaneous equations we're finding the coordinates (\(x\) and \(y\)) of the point(s) of intersection of a *parabola* and a *line*.

The method for solving such simultaneous equations, and therefore for finding the coordinates of the point(s) of intersection of a parabola and a line, is shown in the following *tutorials*.

In this *example* we solve the following pair of *simultaneous equations*:
\[\begin{aligned}
& y = x^2 + 5x - 7 \\
& y = 2x + 3
\end{aligned}\]

In this *example* we solve the following pair of *simultaneous equations*:
\[\begin{aligned}
& y = x^2 + 4x - 9 \\
& 2x - y = 6
\end{aligned}\]

We now learn how to solve simultaneous of the type:
\[\begin{aligned} & x^2+y^2 = 5 \\ & x + y = 1 \end{aligned} \]
Again, we use the * method of substtution*.

When solving this type of pair of simultaneous equations we're finding the coordinates (\(x\) and \(y\)) of the ** point(s) of intersection of a circle and a line**.

The method for solving such simultaneous equations, and therefore finding the coordinates of the point(s) of intersection of a circle and a straight line, is explained in the following tutorial.

In this *example* we solve the following pair of *simultaneous equations*:
\[\begin{aligned}
& x^2 + y^2 = 5 \\
& x + y = 1
\end{aligned}\]

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