Question

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

Answer 1

We have the system

`\begin{gathered} y=(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((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=(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)`