solve the system by substitution. \n$4x + y = 42$\n$y = x + 7$
solve the system by substitution. \n$4x + y = 42$\n$y = x + 7$
Answer
Explanation:
Step1: Substitute ( y = x + 7 ) into ( 4x + y = 42 )
Substitute ( y ) in the first equation with ( x + 7 ), we get ( 4x+(x + 7)=42 ).
Step2: Simplify and solve for ( x )
Simplify the left - hand side of the equation: ( 4x+x + 7=42), which is ( 5x+7 = 42 ). Subtract 7 from both sides: ( 5x=42 - 7=35 ). Divide both sides by 5: ( x=\frac{35}{5}=7 ).
Step3: Substitute ( x = 7 ) into ( y=x + 7 ) to find ( y )
Substitute ( x = 7 ) into ( y=x + 7 ), we get ( y=7 + 7=14 ).
Answer:
The solution of the system is ( x = 7 ) and ( y = 14 )