Solve by Substitution 0.2x+y=5.8 , 0.9x-2y=-6.4

Problem

{[0.2*x+y=5.8],[0.9*x−2*y=−6.4])

Solution

1. Isolate the variable y in the first equation.

0.2*x+y=5.8

y=5.8−0.2*x

2. Substitute the expression for y into the second equation.

0.9*x−2*(5.8−0.2*x)=−6.4

3. Distribute the −2 into the parentheses.

0.9*x−11.6+0.4*x=−6.4

4. Combine the x terms and add 11.6 to both sides to isolate the x term.

1.3*x−11.6=−6.4

1.3*x=5.2

5. Divide by 1.3 to find the value of x

x=5.2/1.3

x=4

6. Substitute x=4 back into the isolated equation for y

y=5.8−0.2*(4)

y=5.8−0.8

y=5

Final Answer

(x,y)=(4,5)

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