Question

Solve the system of equations :
$2x+5y=4;5x-7y=-29$

• A. $(-4,3)$
• B. $(-1,2)$
• C. $(-3,3)$
• D. $(-3,2)$

Answer 1

The correct option is D $(-3,2)$

$2x+5y=4$ ........... (1)
$5x-7y=-29$ ............ (2)
Let's form an equivalent system where the second equation has no x-term. First we can multiply eq. (2) by -2.
$2x+5y=4$ ............ (3)
$-10x+14y=58$ ........... (4)
Now we can replace eq. (4) with an equation that we form by multiplying eq. (3) by 5 and then adding that result to eq. (4)
$2x+5y=4$ ............ (5)
$29y=78$ ............ (6)
From eq. (6) we can find the value of y.
$39y=78\Rightarrow y=2$
Now we can substitute 2 for y in eq. (5)
$2x+5y=4$
$2x+5\left(2\right)=4$
$2x=-6\Rightarrow x=-3$
The solution set is $(-3,2)$.