Answer:
[tex](8,1)[/tex]
Step-by-step explanation:
We have been given a system of linear equations:
[tex]2x+4y=20...(1)[/tex]
[tex]3x+2y=26...(2)[/tex]
We will use substitution method to solve linear equation. From equation (1) we will get,
[tex]x=\frac{20-4y}{2}[/tex]
Substituting this value in equation (2) we will get,
[tex]3*\frac{20-4y}{2}+2y=26[/tex]
[tex]\frac{60-12y}{2}+2y=26[/tex]
Let us have a common denominator.
[tex]\frac{60-12y}{2}+\frac{2*2y}{2}=26[/tex]
[tex]\frac{60-12y}{2}+\frac{4y}{2}=26[/tex]
[tex]\frac{60-12y+4y}{2}=26[/tex]
[tex]\frac{60-8y}{2}=26[/tex]
[tex]\frac{60-8y}{2}*2=26*2[/tex]
[tex]60-8y=52[/tex]
[tex]60-60-8y=52-60[/tex]
[tex]-8y=-8[/tex]
Upon dividing both sides by [tex]-8[/tex] we will get,
[tex]\frac{-8y}{-8}=\frac{-8}{-8}[/tex]
[tex]y=1[/tex]
Upon substituting [tex]y=1[/tex] in equation (1) we will get,
[tex]2x+4*1=20[/tex]
[tex]2x+4=20[/tex]
[tex]2x+4-4=20-4[/tex]
[tex]2x=16[/tex]
Upon dividing both sides of the equation by 2 we will get,
[tex]\frac{2x}{2}=\frac{16}{2}[/tex]
[tex]x=8[/tex]
Therefore, the solution of our given system of equations is [tex](8,1)[/tex].
