The idea is to find a linear combination a_1(5, -6) + a_2(-2, -2) = (-6, 2)
It boils down to a system of equations:
Take the augmented matrix:
<span>[<span><span>5<span>−6</span></span><span><span>−2</span><span>−2</span></span><span><span>−6</span>2</span></span>]</span>
Reduced form:
<span>[<span><span>10</span><span>01</span><span><span>−<span>811</span></span><span>1311</span></span></span>]</span>
-(8/11)*(5, -6) + (13/11)*(-2, -2) = (-6, 2)
To determine which system of equations would have the same solution, we evaluate each system of equations.
System 1 4x − 5y = 2, 3x − y = 8
x = 38/11
y = 26/11
<span>System 2 4x − 5y = 2, 3x − 2y = 1
x = 1/7
y = -2/7
System 3 4x − 5y = 2, 3x − 8y = 4
x = -4/17
y = -10/17
System 4 4x − 5y = 2, 10x − 9y = 4
x = 1/7
y = -2/7
</span><span>
Therefore, the correct answer is option 3. </span><span>System 2 and system 4 are equal, because the second equation in system 4 is obtained by adding the first equation in system 2 to two times the second equation in system 2.
4x− 5y = 2 2( 3x − 2y = 1)
----------------------- 10x - 9y = 4</span>
Answer:
a
Step-by-step explanation:
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Answer:
C
Step-by-step explanation:
