Exercise 6 Page 227

We want to solve the given system of linear equations using a graphing calculator. 2.6x+1.3y=7.8 & (I) 1.2x-3.6y=12 & (II) Remember that we can also solve systems of linear equations using graphing, elimination, or substitution. To solve the system using a graphing calculator, both of the equations should be written in slope-intercept form. Therefore, we need to isolate the y-variable on the left-hand side of each equation. Now that the y-variable is isolated in both equations, we can format the equation in slope-intercept form.

To solve the system using a graphing calculator, we first press the Y= button and type the firs equation in one of the rows and the second equation in another row. After writing the equations, we can push GRAPH to draw them.

We know that the solution to the system of linear equations is the point of intersection of the graphs of the equations.To find the point of intersection on a calculator, we push 2nd and CALC and choose the fifth option, intersect.

The graphs intersect at the point (4,- 2). Finally, we will check if this point is a solution to the system of equations. To do this, we will substitute 4 for x and - 2 for y in each equation and simplify.

2.6x+1.3y=7.8 & (I) 1.2x-3.6y=12 & (II)

SubstituteII

x= 4, y= - 2

2.6( 4)+1.3( - 2)? =7.8 1.2( 4)-3.6( - 2)? =12

▼

(I), (II): Evaluate

(I), (II): a(- b)=- a * b

2.6(4)+(- 2.6)? =7.8 1.2(4)-(- 7.2)? =12

(I), (II): Multiply

10.4+(- 2.6)? =7.8 4.8-(- 7.2)? =12

AddNeg

(I): a+(- b)=a-b

10.4-2.6? =7.8 4.8-(- 7.2)? =12

SubNeg

(II): a-(- b)=a+b

10.4-2.6? =7.8 4.8+7.2? =12

(I), (II): Add and subtract terms

7.8=7.8 ✓ 12=12 ✓

Simplifying the expressions resulted in identities. Therefore, the solution to this system of equations is (4,- 2).