The solution to the system of equation is [tex](\frac{5}{6},\frac{61}{12} )[/tex]
Explanation:
Given that the two equations are [tex]2x+4y=22[/tex] and [tex]13x+2y=21[/tex]
We need to determine the solution to the system of equations.
It is also given that to start by solving the equations, by multiplying the second equation by 2.
Thus, we have,
[tex]2(13x+2y=21) \implies 26x+4y=42[/tex] --------(3)
Let us subtract the first equation from the equation (3), we have,
[tex]-24x=-20[/tex]
[tex]x=\frac{20}{24}[/tex]
[tex]x=\frac{5}{6}[/tex]
Thus, the value of x is [tex]x=\frac{5}{6}[/tex]
Substituting [tex]x=\frac{5}{6}[/tex] in the equation [tex]2x+4y=22[/tex] , we have,
[tex]2(\frac{5}{6}) +4y=22[/tex]
Simplifying, we have,
[tex]\frac{5}{3} +4y=22[/tex]
[tex]4y=22-\frac{5}{3}[/tex]
[tex]4y=\frac{66-5}{3}[/tex]
[tex]4y=\frac{61}{3}[/tex]
[tex]y=\frac{61}{12}[/tex]
Thus, the value of y is [tex]y=\frac{61}{12}[/tex]
Hence, the solution to the system of the equation is [tex](\frac{5}{6},\frac{61}{12} )[/tex]
