Answer :
Answer:
The values are [tex]x=\frac{7}{2}[/tex] and [tex]y=\frac{5}{2}[/tex]
The solution is ([tex]\frac{7}{2}[/tex],[tex]\frac{5}{2}[/tex])
Step-by-step explanation:
Given equations are [tex]5x=7y\hfill (1)[/tex] and
[tex]x+7y=21\hfill (2)[/tex]
To solve the given equations by elimination method:
Equation (1) can be written as [tex]5x-7y=0\hfill (3)[/tex] and
Now multiply the equation (2) into 5 we get
[tex]5x+35y=105\hfill (4)[/tex]
Subtracting equations (3) and (4) we get
[tex]5x-7y=0[/tex]
[tex]5x+35y=105[/tex]
_________________
-42y=-105
[tex]y=\frac{105}{42}[/tex]
Therefore [tex]y=\frac{5}{2}[/tex]
Substitute the value [tex]y=\frac{5}{2}[/tex] in equation (1) we get
[tex]5x=7\times \frac{5}{2}[/tex]
[tex]5x=\frac{35}{2}[/tex]
[tex]x=\frac{35}{2\times 5}[/tex]
[tex]x=\frac{7}{2}[/tex]
Therefore [tex]x=\frac{7}{2}[/tex] and [tex]y=\frac{5}{2}[/tex]
The solution is ([tex]\frac{7}{2}[/tex],[tex]\frac{5}{2}[/tex])