Graphical method of finding solutions.

Subtracting the equations gives \(2x=10\), so \(x=5\) and \(y=6\). On the graph this is where the paths meet.

Subtracting the second from the first gives \(y=7\), then \(x+7=11\) gives \(x=4\). In any context, the common point is the solution.

Subtracting the equations gives \(x=6\), then \(6+3y=17\) gives \(y=\frac{11}{3}\). Fraction coordinates can also be graphical solutions.

Small errors can occur while reading fractional or decimal coordinates from a graph. Keep the scale clear and read the point carefully.

A point is always written in \(\left(x,y\right)\) order. Reversing coordinates makes the solution wrong.

Subtracting the equations gives \(2x=12\), so \(x=6\) and \(y=2\). This is the intersection point on the graph.

To find the \(y\)-intercept, put \(x=0\). Then \(7(0)-2y=14\), so \(-2y=14\) and \(y=-7\). Therefore, the \(y\)-intercept is \(\left(0,-7\right)\). Option B has the wrong sign, while \(\left(2,0\right)\) and \(\left(-2,0\right)\) represent possible \(x\)-intercept points, not the \(y\)-intercept. Exam tip: Set \(x=0\) to find the \(y\)-intercept.

Dividing the first equation by (2) gives (x+3y=9), while the second is (x+3y=12). Hence the lines are parallel and have no solution.

\(\frac{7}{2}=3.5\) and \(\frac{5}{2}=2.5\). While reading a graph, understand the relation between fraction and decimal forms.

Putting \(x=-3\) gives \(2\left(-3\right)+y=4\), so \(y=10\). In a vertical line, the value of (x) is already fixed.

Subtracting the second equation from the first gives \(y=5\), then \(x+5=8\) gives \(x=3\). In a real situation, the meeting point is the graphical solution.

Subtracting the equations gives \(3x=15\), so \(x=5\) and \(y=5\). On the graph, this is the intersection point of both lines.

Solving both equations gives \(x=\frac{25}{7}\) and \(y=\frac{23}{7}\). On the graph this is the intersection point.

From the second equation, \(x=23-5y\). Substituting this into the first equation gives \(3(23-5y)-2y=4\), or \(69-17y=4\), so \(y=\frac{65}{17}\). Therefore, \(x=23-5\left(\frac{65}{17}\right)=\frac{66}{17}\). Hence, the two lines intersect at \(\left(\frac{66}{17},\frac{65}{17}\right)\). In option B, the value of \(x\) is incorrect. Exam tip: The graphical solution is the common point of the two lines; verify the point by substituting it into both equations.

\(\left(2,3\right)\) satisfies both equations. In difficult options, direct substitution is the fastest check.

Elimination gives \(19y=69\) and \(x=\frac{106}{19}\). Fraction coordinates can also be graphical solutions.

(\frac{a_1}{a_2}=\frac{b_1}{b_2}=2), but (\frac{c_1}{c_2}=\frac{10}{7}). Hence the lines are parallel and inconsistent.

Dividing the first equation by (3) gives (2x-3y=5). Therefore both are the same line and have infinitely many solutions.

Multiplying the first equation by (2) gives (6x-2y=10), while the second is (6x-2y=11). Hence the lines are parallel and have no solution.

For the x-intercept, put \(y=0\): \(7x=28\), giving \(x=4\), so the point is \((4,0)\). For the y-intercept, put \(x=0\): \(-4y=28\), giving \(y=-7\), so the point is \((0,-7)\). Therefore, option A is correct. Exam tip: check the sign of the y-intercept and maintain the stated order—x-intercept first, y-intercept second.