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QuestionSolve for (x,y)(x, y) in the system: 5x−3y=145x - 3y = 14 and y=x+8y = x + 8.

Studdy Solution

STEP 1

Assumptions1. We have a system of two linear equations a. 5x−3y=145x -3y =14 b. y=x+8y = x +8 . We need to find the values of xx and yy that satisfy both equations.

STEP 2

We can use the method of substitution to solve this system. This involves solving one of the equations for one variable and then substituting this expression into the other equation. The second equation is already solved for yy, so we can substitute x+8x +8 for yy in the first equation.
5x−(x+8)=145x -(x +8) =14

STEP 3

Next, we simplify the left side of the equation by distributing the −3-3 to both xx and 88.
5x−3x−24=145x -3x -24 =14

STEP 4

Combine like terms on the left side of the equation.
2x−24=142x -24 =14

STEP 5

Add 2424 to both sides of the equation to isolate 2x2x on one side.
2x=14+242x =14 +24

STEP 6

implify the right side of the equation.
2x=382x =38

STEP 7

Divide both sides of the equation by 22 to solve for xx.
x=38/2x =38 /2

STEP 8

Calculate the value of xx.
x=19x =19

STEP 9

Now that we have the value of xx, we can substitute 1919 for xx in the second equation to solve for yy.
y=19+8y =19 +8

STEP 10

Calculate the value of yy.
y=27y =27The solution to the system of equations is (x,y)=(19,27)(x, y) = (19,27).

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