Answer
\[\left\{ \left( -2,3 \right) \right\}\]
Work Step by Step
To find the solution of provided system of equation by substitution method use the following steps:
Step1:
The second equation, \[y=2x+7\], is solved for the y in terms of x.
Step 2:
Substitute the value of \[y=2x+7\] into the other equation \[2x-3y=-13\]. The equation became in one variable x. Solve the equation for x.
\[\begin{align}
& 2x-3y=-13 \\
& 2x-3\left( 2x+7 \right)=-13 \\
& 2x-6x-21=-13 \\
& -4x=21-13
\end{align}\]
Simplify the above equation:
\[\begin{align}
& -4x=21-13 \\
& -4x=8 \\
& x=-2
\end{align}\]
Step 3:
Now, substitute the value of x obtained in step2, \[y=2x+7\]:
\[\begin{align}
& y=2x+7 \\
& y=2\cdot \left( -2 \right)+7 \\
& y=-4+7 \\
& y=3
\end{align}\]
Step 4:
The value of x and y obtained in step2 and step3, is the solution of the provided system of equations.
Hence \[\left\{ \left( -2,3 \right) \right\}\]is the required solution.
Step 5:
Now, to verify that the obtained solution is correct, substitute the values of x and y in both equations.
Put \[x=-2\text{ and }y=3\]
\[\begin{align}
& 2x-3y=-13 \\
& 2\cdot \left( -2 \right)-3\cdot 3=-13 \\
& -4-9=-13 \\
& -13=-13
\end{align}\]
\[\begin{align}
& y=2x+7 \\
& 3=2\cdot \left( -2 \right)+7 \\
& 3=-4+7 \\
& 3=3
\end{align}\]
Since, \[\left( -2,3 \right)\]satisfies both equations, the set \[\left( -2,3 \right)\]is the solution of the provided system of equations.
