Question

solve each system of equations using substitution. y= 1/2x+4 2y+2x=2

Answer 1

We have the system

$\begin{gathered} y=\frac{1}{2}x+4 \\ 2y+2x=2 \end{gathered}$

We solve it by substituting the value of y from the first equation into the second.

substituting = 1/2x+4 into 2y+2x=2​ gives us

$2(\frac{1}{2}x+4)+2x=2$

expanding the above LHS of the above gives

$x+8+2x=2$$3x+8=2$

subtracting 8 from both sides gives

$3x=-6$

finally, dividing both sides by 3 results in

$x=-2.$

And we have the value of x. Now let us find y.

Substituting x = -2 into y= 1/2x+4 gives

$y=\frac{1}{2}(-2)+4$$\begin{gathered} y=-1+4 \\ \therefore y=3. \end{gathered}$

Thus we have the value of both x and y, and now we are in a position to write the solution to the system.

The solution to the system is

$(-2,3)$