solve the system of equations:\ny = 6x\n4x + y = 7

Explanation:

Step1: Substitute ( y = 6x ) into ( 4x + y = 7 )

Substitute ( y ) in the second equation with ( 6x ) from the first equation. So we get ( 4x + 6x = 7 ).

Step2: Combine like terms

Combine ( 4x ) and ( 6x ) to get ( 10x = 7 ).

Step3: Solve for ( x )

Divide both sides of the equation ( 10x = 7 ) by 10. So ( x=\frac{7}{10}=0.7 ).

Step4: Solve for ( y )

Substitute ( x = 0.7 ) into ( y = 6x ). Then ( y = 6\times0.7 = 4.2 ).

Answer:

The solution to the system of equations is ( x = 0.7 ), ( y = 4.2 ) (or in fraction form ( x=\frac{7}{10} ), ( y=\frac{21}{5} ))