Question

Solve the system of equations by the substitution method. Then use the solution to evaluate the expression 2x(−3+y).

6x+2y+1=13+10y−x
5x=y+26−2x
The value of the expression is....

Answer 1

`\left\{\begin{array}{ccc}6x+2y+1=13+10y-x\\5x=y+26-2x\end{array}\right\\\\\left\{\begin{array}{ccc}6x+x+2y-10y=13-1\\5x+2x-26=y\end{array}\right\\\left\{\begin{array}{ccc}7x-8y=12&(**)\\y=7x-26&(*)\end{array}\right\\\\\text{substitute}\ (*)\ \text{to}\ (**)\\\\7x-8(7x-26)=12\\7x-(8)(7x)-(8)(-26)=12\\7x-56x+208=12\\-49x=12-208\\-49x=-196\qquad\text{divide both sides by (-49)}\\\boxed{x=4}\\\\\text{put the value of x to}\ (*)\\\\y=7(4)-26\\y=28-26\\\boxed{y=2}\\\\\boxed{x=4\ and\ y=2}`

`\text{Put the values of x and y to the expression}\ 2x(-3+y):\\\\2(4)(-3+2)=8(-1)=-8\\\\Answer:\ \boxed{\text{The valuie of the expression is -8}}`