From the given system of linear equations, we have;
- a. x ≈ 0.697, y ≈ 5.84
- b. x ≈ 2.48, y ≈ -1.82
- c. x ≈ 4.56, y ≈ -15.35
<h3>How can technology be used to solve the given equations?</h3>
a. The system of linear equations can be expressed as follows;
y = 22•x - 9.5
y = 2.5•x + 4.1
Rewriting the equations to have the constants on the right, we have;
y - 22•x = - 9.5
y - 2.5•x = 4.1
Solving the above equations using matrices method on a calculator gives;
By direct solving, we have;
22•x - 9.5 = 2.5•x + 4.1
22•x - 2.5•x = 4.1 + 9.5
19.5•x = 13.6
x = 13.6 ÷ 19.5 ≈ 0.697
y = 22•x - 9.5
y = 22×(13.6/19.5) - 9.5 ≈ 5.84
b. 8•x + y - 18 = 0
5•x + 9•y + 4 = 0
Rewriting gives;
8•x + y = 18
5•x + 9•y = -4
Solving with technology gives,;
Solving directly gives;
- y = 18 - 8•x
- y = -(5•x + 4)/9
Which gives;
18 - 8•x = -(5•x + 4)/9
9×(18 - 8•x) = -(5•x + 4)
162 - 72•x = -(5•x + 4)
5•x - 72•x = -162 - 4 = -166
67•x = 166
x = 166 ÷ 67 ≈ 2.478
y = 18 - 8•x
Therefore;
y = 18 - 8 × (166 ÷ 67) ≈ -1.82
- y ≈ -1.82
c. 6•x + y = 12
5•x + 8•y = -100
Solving the above linear system using technology, we have;
Solving directly, we have;
y = 12 - 6•x
5•x + 8•y = -100
y = (-100 - 5•x)/8
12 - 6•x = (-100 - 5•x)/8
8 × (12 - 6•x) = (-100 - 5•x)
96 - 48•x = (-100 - 5•x)
48•x - 5•x = 96 + 100
43•x = 196
x = 196/43 ≈ 4.56
y = 12 - 6•x
Therefore;
y = 12 - 6×(196/43) ≈ -15.35
Learn more about linear equations here:
brainly.com/question/2226590
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