Question

solve using elimination.\
-3x + y = 10\
7x - 10y = 15\
(\boxed{ }, \boxed{ }))

Explanation:

Step1: Multiply first equation by 10

To eliminate \( y \), we multiply the first equation \(-3x + y = 10\) by 10. This gives us:
\(10\times(-3x + y)=10\times10\)
\(-30x + 10y = 100\)

Step2: Add the two equations

Now we add the new equation \(-30x + 10y = 100\) to the second equation \(7x - 10y = 15\).
\((-30x + 10y)+(7x - 10y)=100 + 15\)
Simplify the left - hand side: \(-30x+7x+10y - 10y=-23x\)
Simplify the right - hand side: \(115\)
So we have the equation \(-23x = 115\)

Step3: Solve for x

Divide both sides of the equation \(-23x = 115\) by \(-23\):
\(x=\frac{115}{-23}=-5\)

Step4: Substitute x into first equation

Substitute \(x = - 5\) into the first equation \(-3x + y = 10\):
\(-3\times(-5)+y = 10\)
\(15 + y = 10\)

Step5: Solve for y

Subtract 15 from both sides of the equation \(15 + y = 10\):
\(y=10 - 15=-5\)

Answer:

\((-5, -5)\)