Question

Can you solve the system of linear equations by substitutionx = 5 - y and 2x + 5y = 4

Answer 1

(7, -2)

Explanation:

To find the solution to the system using substitution, we put in the value of x from x = 5 - y into 2x + 5y = 4. This gives

`\begin{gathered} 2x+5y=4 \\ 2(5-y)+5y=4 \\ \end{gathered}`

Simplifying the above gives

`10-2y+5y=4`
`10+3y=4`

Subtracting 10 from both sides gives

`3y=4-10`
`3y=-6`

dividing both sides by 3 gives

`\boxed{y=-2}`

With the value of y in hand, we now use it in x = 5 -y to find the value of x.

Substituting the y = -2 into x = 5 - y gives

`x=5--2`
`\boxed{x=7}`

Hence, the solution to our system is

`(7,-2)`