Certainly! Let's solve the given system of equations using the substitution method. The equations are:
[tex]\[
\begin{array}{l}
y = 4x + 3 \\
y = 7 + 3x \\
\end{array}
\][/tex]
Since both equations are set equal to [tex]\( y \)[/tex], we can set their right-hand sides equal to each other:
[tex]\[
4x + 3 = 7 + 3x
\][/tex]
Now we need to solve for [tex]\( x \)[/tex]. First, let's isolate [tex]\( x \)[/tex] on one side of the equation:
[tex]\[
4x + 3 = 7 + 3x
\][/tex]
Subtract [tex]\( 3x \)[/tex] from both sides:
[tex]\[
4x - 3x + 3 = 7
\][/tex]
Simplify:
[tex]\[
x + 3 = 7
\][/tex]
Subtract 3 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
x = 4
\][/tex]
Now that we have the value of [tex]\( x \)[/tex], we substitute it back into either of the original equations to solve for [tex]\( y \)[/tex]. Let's use the first equation:
[tex]\[
y = 4x + 3
\][/tex]
Substitute [tex]\( x = 4 \)[/tex]:
[tex]\[
y = 4(4) + 3
\][/tex]
Calculate [tex]\( 4(4) \)[/tex]:
[tex]\[
y = 16 + 3
\][/tex]
Add 3:
[tex]\[
y = 19
\][/tex]
Thus, the solution to the system of equations is:
[tex]\[
(x, y) = (4, 19)
\][/tex]
So the ordered pair that solves the system is [tex]\( (4, 19) \)[/tex].
