Answer:
[tex]a=10[/tex]
Step-by-step explanation:
Equation 1: [tex]2a+3b=-1[/tex]
Equation 2: [tex]4a+2b=26[/tex]
Subtract 3b from both sides in Equation 1:
[tex]2a=-1-3b[/tex]
Divide both sides by 2:
[tex]\frac{2a}{2}=-\frac{1-3b}{2}[/tex]
[tex]a=\frac{-1-3b}{2}[/tex]
Substitute this into Equation 2:
[tex]4* \frac{-1-3b}{2}+2b=26[/tex]
[tex]2\left(-3b-1\right)+2b=26[/tex]
[tex]-6b-2+2b=26[/tex]
[tex]-4b-2=26[/tex]
Add 2 to both sides:
[tex]-4b=28[/tex]
Divide both sides by -4:
[tex]\frac{-4b}{-4}=\frac{28}{-4}[/tex]
[tex]b=-7[/tex]
We know that [tex]a=\frac{-1-3b}{2}[/tex]. Plug in b = -7 value:
[tex]a=\frac{-1-3\left(-7\right)}{2}[/tex]
[tex]a=\frac{-1+3\cdot \:7}{2}[/tex]
[tex]a=\frac{20}{2}[/tex]
[tex]a=10[/tex]
