Question

Solve the system. Estimate the solution first. Enter whole numbers for the estimated solution and Improper fractions in simplest form for the algebraic solution. 3x + y =2 5x - y = 8 The estimated solution is ____, ____The algebraic solution is ____, ____

Answer 1

Problem

3x + y = 2

5x - y = 8

Method

Substitution method

Solution

step 1

name the equations

3x + y = 2............................................ 1

5x - y = 8 ............................................ 2

Step 2

choose one equation and make one of the variable subject of relation

5x - y = 8

5x - 8 = y

y = 5x - 8

Step 3

substitute y in equation 1

equation 1 3x + y = 2

3x + 5x - 8 = 2

collect like terms

3x + 5x = 2 + 8

8x = 10

x = 10/8

x = 5/4

Step 4

substitute in any equation to find y

y = 5x - 8

`\begin{gathered} y\text{ =5 x }(5)/(4)\text{ - 8} \\ y\text{ = }(25)/(4)\text{ - 8} \\ y\text{ = }\frac{25\text{ - 4x8}}{4} \\ y\text{ = }\frac{25\text{ - 32}}{4} \\ y\text{ = }(-7)/(4) \end{gathered}`

x = 5/4 and y = -7/4

Estimated solution is the approximate value in whole numbers

x = 5/4 = 1.25 estimated value of x.= 1

y = -7/4 = -1.75 estimated value of y = -2