Question

What is the solution to the system of equations? Use the substitution method. {y=−2x+5 3x−4y=2

Answer 1

We have that
y=−2x+5 --------> equation 1
3x−4y=2---------> equation 2
substituting 1 in 2
3x-4*(-2x+5)=2--------> 3x+8x-20=2--------> 11x=22-----> x=2
y=-2x+5-----> -2*2+5-----> y=1

the solution is
x=2
y=1

Answer 2

$LINEAR \: \: EQUATIONS \: \: IN \: \: TWO \: \: \\ VARIABLES \\ \\ \\\\Given \: \: - \\ \\ y \: = - 2x + 5 \: \: \: - - - eq.(1) \\ \\ \: 3x - 4y = 2 \: \: \: \: - - - eq.(2) \\ \\ Using \: \: substitution \: \: method \: , \: \\ Putting \: \: \: eq.(1) \: \: in \: \: eq.(2) \\ \\ 3x - 4 \: ( - 2x + 5) = 2 \\ \\ 3x + 8x - 20 = 2 \\ \\ 11x \: - 20 \: \: = \: \: 2 \\ \\ 11x \: \: = \: \: 22 \: \: \\ \\ x \: \: = \: \: \frac{22}{11} \: \: = \: \: 2 \: \: \: - - - eq.(3) \\ \\ Putting \: \: eq.(3) \: \: in \: \: eq.(1) \: \\ \\ We \: get \: \: - \\ \\ y = - 2(2) + 5 = 5 - 4 = 1 \\ \\ \\ Hence \: \\ \\ \: || \: \: x = 2 \: \: || \: \: \: \: and \: \: \: || \: \: y = 1 \: \: || \: \: \: \: \: \: \: \: Ans.$