The solution to the system of equations is [tex](\frac{5}{3},\frac{14}{3})[/tex]
Explanation:
Given that the system of equations are [tex]y=4x-2[/tex] and [tex]y=x+3[/tex]
We need to determine the solution to the system of equations.
The solution of the system of equations can be determined using the substitution method.
Thus, we have,
[tex]4x-2=x+3[/tex]
Simplifying, we get,
[tex]3x-2=3[/tex]
[tex]3x=5[/tex]
[tex]x=\frac{5}{3}[/tex]
Thus, the value of x is [tex]\frac{5}{3}[/tex]
Substituting [tex]x=\frac{5}{3}[/tex] in the equation [tex]y=x+3[/tex], we get,
[tex]y=\frac{5}{3}+3[/tex]
Simplifying, we get,
[tex]y=\frac{5+9}{3}[/tex]
[tex]y=\frac{14}{3}[/tex]
Thus, the value of y is [tex]\frac{14}{3}[/tex]
Hence, the solution to the system of equations is [tex](\frac{5}{3},\frac{14}{3})[/tex]
