Question

solve the system of equations by the substitution method.\

$$\begin{cases}x - 3y = -2\\\\3x - 10y = -10\\end{cases}$$

Explanation:

Step1: Solve for x from first equation

From \( x - 3y = -2 \), we can express \( x \) as \( x = 3y - 2 \).

Step2: Substitute x into second equation

Substitute \( x = 3y - 2 \) into \( 3x - 10y = -10 \). So we have \( 3(3y - 2)-10y=-10 \).

Step3: Simplify and solve for y

Expand the left - hand side: \( 9y-6 - 10y=-10 \). Combine like terms: \( -y-6=-10 \). Add 6 to both sides: \( -y=-10 + 6=-4 \). Multiply both sides by - 1: \( y = 4 \).

Step4: Substitute y back to find x

Substitute \( y = 4 \) into \( x = 3y-2 \). Then \( x=3\times4 - 2=12 - 2 = 10 \).

Answer:

The solution of the system of equations is \( x = 10,y = 4 \) (or the ordered pair \((10,4)\))