To solve this question using the addition/elimination method, follow the steps below.
Step 01: Multiply the first equation by 2.
[tex]\begin{gathered} (5x-2y)\cdot2=3\cdot2 \\ 5x\cdot2-2y\cdot2=6 \\ 10x-4y=6 \end{gathered}[/tex]
Step 02: Add both equations to eliminate y.
[tex]\begin{gathered} +10x-4y=6 \\ -3x+4y=1 \\ 7x+0=7 \\ 7x=7 \end{gathered}[/tex]
Step 03: Isolate x in the equation above.
To do it, divide both sides by 7.
[tex]\begin{gathered} \frac{7x}{7}=\frac{7}{7} \\ 1x=1 \\ x=1 \end{gathered}[/tex]
Step 04: Choose one equation to substitute x by 1 and find y.
Choosing the first equation:
[tex]\begin{gathered} 5x-2y=3 \\ 5\cdot1-2y=3 \\ 5-2y=3 \end{gathered}[/tex]
Subtracting 5 from both sides, then dividing both sides by -2:
[tex]\begin{gathered} 5-2y-5=3-5 \\ -2y=-2 \\ \frac{-2}{-2}y=\frac{-2}{-2} \\ y=1 \end{gathered}[/tex]
Answer:
x = 1.
y = 1.
